révision scientifique complète (editorial board, 2026-10-17)
WP 6 v1.0 (May 2026) -> v1.1 (October 2026). Panel du VAR reconstruit sur 2 514 jours de bourse (sans report des fins de semaine), log RV, bootstrap résiduel (IC 90 %), grille de robustesse, fenêtres 200/250/500 jours, 4 régimes + années civiles, Granger HAC, analyse intrajournalière avec conversion heure de l'Est -> UTC et régressions ordonnées par session ; titre « Fixed Income » -> « Foreign Exchange » ; bibliographie convertie en references.bib (natbib/aer), 45 -> 70 références vérifiées (Crossref/DOI) ; docs/REVIEW-REPORT.md + docs/CHANGELOG-REVISION.md. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
74 changed files +9,746 −696
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README.md
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@@ -1,16 +1,16 @@ | ||
| 1 | 1 | <!-- Author: Simon-Pierre Boucher — simon-pierre.boucher@uqo.ca --> |
| 2 | 2 | # 🌐 Intraday Volatility Transmission Across Asset Classes |
| 3 | 3 | |
| 4 | −**UQO Working Paper No. 6** — *A Connectedness Analysis of Equities, Fixed Income, Commodities, and Cryptocurrencies* | |
| 4 | +**UQO Working Paper No. 6** — *A Connectedness Analysis of Equities, Foreign Exchange, Commodities, and Cryptocurrencies* | |
| 5 | 5 | |
| 6 | −[-b31b1b?logo=latex&logoColor=white)](paper/main.pdf) | |
| 6 | +[-b31b1b?logo=latex&logoColor=white)](paper/main.pdf) | |
| 7 | 7 | [](requirements.txt) |
| 8 | 8 | [](data/raw/README.md) |
| 9 | −[](scripts/) | |
| 9 | +[](scripts/) | |
| 10 | 10 | [](https://uqo.ca) |
| 11 | 11 | [](mailto:simon-pierre.boucher@uqo.ca) |
| 12 | 12 | |
| 13 | −> **TL;DR** — Daily realized volatility is built from 5-minute bars (2008–2026) for 10 instruments spanning equity futures (ES, NQ), FX (EURUSD, USDJPY, GBPUSD), commodities (GC, CL), crypto (BTC, ETH) and the VIX, and fed to the Diebold–Yilmaz (2012) connectedness framework (VAR(4), 10-day GFEVD). Total spillover is **55.4 %**; ES and NQ are the dominant transmitters (**+26.8 / +19.7 pp** net), the VIX the main receiver (**−23.4 pp**), and crypto stays largely isolated (own-shock share > 77 %). Connectedness peaks at **81.6 %** in February 2018; during COVID USD/JPY becomes the top shock originator and in the 2022 hiking cycle Bitcoin turns into a net transmitter (+7.9 pp). | |
| 13 | +> **TL;DR** — Daily realized volatility is built from 5-minute bars (2008–2026) for 10 instruments — equity futures (ES, NQ), FX (EURUSD, USDJPY, GBPUSD), commodities (GC, CL), crypto (BTC, ETH) and the VIX — and the Diebold–Yilmaz connectedness of **log** RV is estimated on the **2,514 trading days** common to all series (2016-03 → 2026-03; VAR(4), 10-day GFEVD, residual-bootstrap 90 % intervals). Total spillover is **54.8 %** [53.1, 56.9]. ES and NQ are the only robust net transmitters (**+36.0 / +25.6 pp**); the RV of the VIX (**−20.6**), crude oil (−14.2) and sterling (−13.2) are net receivers; BTC/ETH net positions are indistinguishable from zero. Crypto's exposure to traditional assets rises from < 10 % of forecast-error variance (2017, 2019) to 20–46 % (2020–2025), with the flow running **from U.S. equities to crypto**: in the spot-ETF era BTC is a significant net receiver (−12.4 [−20.4, −2.1]). Connectedness peaks in 2025 (71.5 %). Intraday (time stamps converted from Eastern to UTC), the U.S. cash session generates 53–63 % of equity/VIX daily variance while bitcoin's hourly profile is nearly flat (peak/trough 1.2); weekend bitcoin volatility does not predict Monday equity volatility. | |
| 14 | 14 | |
| 15 | 15 | --- |
| 16 | 16 | |
@@ -18,101 +18,113 @@ | ||
| 18 | 18 | |
| 19 | 19 | | Item | Value | |
| 20 | 20 | |---|---| |
| 21 | −| Version | 1.0 (May 2026) | | |
| 21 | +| Version | **1.1 (October 2026)** — revised 2026-10-17 by the editorial-board review (v1.0: May 2026) | | |
| 22 | 22 | | SSRN | not yet submitted | |
| 23 | −| Journal | — | | |
| 24 | −| Code & data | reproducible from `scripts/01_analysis.py`; raw DuckDB files not redistributed | | |
| 23 | +| Journal | — (realistic targets: IRFA, JIFMIM; see `docs/REVIEW-REPORT.md` §9) | | |
| 24 | +| Code & data | VAR/GFEVD stage fully reproducible from the committed `results/daily_rv_all.csv` (`scripts/02_…`, ≈ 1 min); intraday stage from local 1-minute bars (`scripts/03_…`); raw 5-minute DuckDB files not redistributed | | |
| 25 | 25 | |
| 26 | 26 | ## 🎯 What this paper does |
| 27 | 27 | |
| 28 | −The paper measures how volatility shocks travel across asset classes at the daily frequency, using realized volatility computed from intraday data rather than low-frequency proxies. Ten representative instruments are followed over 2008–2026 and the generalized forecast-error variance decomposition of a VAR is used to build directional, net and total spillover indices: | |
| 28 | +The paper measures how realized-volatility shocks travel across asset classes at the daily frequency, using realized volatility from 5-minute data rather than range- or return-based proxies, and exploits the intraday data a second time to study trading sessions. Ten instruments are followed over 2008–2026; the generalized forecast-error variance decomposition of a VAR on log realized volatility yields directional, net and total spillovers with bootstrap intervals: | |
| 29 | 29 | |
| 30 | 30 | ``` |
| 31 | −RV_{i,t} = Σ_k r²_{i,t,k} (5-min returns) → VAR(4) on log RV → GFEVD(H = 10) → TSI, TO, FROM, NET | |
| 31 | +RV_{i,t} = Σ_k r²_{i,t,k} (5-min) → y = ln √(252·RV) on common trading days → VAR(4), GFEVD(H = 10) → TSI, TO, FROM, NET (+ 90 % bootstrap CI) | |
| 32 | 32 | ``` |
| 33 | 33 | |
| 34 | −Full-sample, rolling (200-day) and regime-specific (pre-COVID, COVID crash, 2022 rate hikes) decompositions are complemented by a trading-session analysis (Asian / European / U.S. hours) and Granger-causality tests between equity futures, the VIX and crypto. | |
| 34 | +Full-sample, robustness-grid (15 specifications), rolling (200/250/500 trading days), regime (pre-COVID, COVID crash, 2022 hikes, spot-ETF era) and calendar-year decompositions are complemented by Granger tests with HAC inference, a UTC-correct hourly/session analysis (Asian / European / U.S.) and session-ordered predictive regressions between equity futures, the VIX and bitcoin. | |
| 35 | 35 | |
| 36 | 36 | ## 🏆 Headline results |
| 37 | 37 | |
| 38 | −| Object | Estimate | | |
| 38 | +| Object | Estimate (v1.1) | | |
| 39 | 39 | |---|---| |
| 40 | −| Total spillover index, full sample | 55.44 % | | |
| 41 | −| Net spillover ES / NQ | +26.80 / +19.72 pp | | |
| 42 | −| Net spillover VIX | −23.37 pp | | |
| 43 | −| Own-shock share BTC, ETH | > 77 % | | |
| 44 | −| Rolling TSI peak | 81.55 % (Feb 2018 volatility implosion) | | |
| 45 | −| COVID crash top transmitter | USD/JPY (+60.29 pp) | | |
| 46 | −| 2022 rate hikes: BTC net spillover | +7.90 pp (net transmitter) | | |
| 47 | −| Granger: equity futures → VIX | F = 19.86, p < 0.001 | | |
| 40 | +| Total spillover index, 2016-03 → 2026-03 (T = 2,514) | 54.8 % [53.1, 56.9] | | |
| 41 | +| Net spillover ES / NQ | +36.0 [29.9, 41.5] / +25.6 [19.0, 31.3] pp | | |
| 42 | +| Net spillover VIX (RV of index changes) / CL / GBPUSD | −20.6 / −14.2 / −13.2 pp (all CIs exclude 0) | | |
| 43 | +| Net spillover BTC / ETH | +1.7 [−3.3, 6.4] / −2.4 [−7.9, 2.1] pp | | |
| 44 | +| Own-shock share BTC / ETH ; BTC↔ETH | 66.7 / 64.9 % ; 27–28 % | | |
| 45 | +| Share of BTC variance from traditional assets | 6.3 % full sample ; 6.8 % (2019) → 34 % (2020) → 46 % (2025) | | |
| 46 | +| Spot-ETF era (2024-01 → 2026-03): NET BTC / ETH | −12.4 [−20.4, −2.1] / −19.5 [−27.7, −9.2] pp | | |
| 47 | +| COVID crash (T = 85, VAR(1)): NET USDJPY | +81.8 [+7.3, +135.3] pp | | |
| 48 | +| Rolling TSI (200 td): mean / min / max | 61.9 % / 50.5 % (2017-10-27) / 73.4 % (2025-09-24) | | |
| 49 | +| Granger ES → RV(VIX) | F = 19.9, HAC Wald 62.8, p < 0.001 | | |
| 50 | +| U.S.-session share of daily variance: ES / NQ / VIX | 53 / 54 / 63 % ; BTC hourly peak/trough = 1.2 | | |
| 51 | +| Weekend BTC RV → Monday ES U.S.-session RV | coef −0.04 (s.e. 0.05), not significant | | |
| 48 | 52 | |
| 49 | 53 | ## 🗂 Repository layout |
| 50 | 54 | |
| 51 | 55 | ``` |
| 52 | 56 | intraday-volatility-connectedness/ |
| 53 | −├── data/ | |
| 54 | −│ ├── raw/ # futures_5min / fx_5min / crypto_5min .duckdb (see data/raw/README.md) — not committed | |
| 55 | −│ └── processed/ | |
| 57 | +├── data/raw/README.md # 4 DuckDB 5-min databases (not committed) + 1-min bars used by 03_ (sibling WP 12) | |
| 56 | 58 | ├── scripts/ |
| 57 | −│ └── 01_analysis.py # RV construction, VAR/GFEVD, rolling & regime analysis, sessions, Granger, figures | |
| 58 | −├── results/ # table1…table4 CSV, daily_rv_all.csv, rolling_total_spillover.csv | |
| 59 | −├── figures/ # fig1…fig7 PNG (copied into paper/figures) | |
| 60 | −└── paper/ # main.tex + sections/ + appendix/ → main.pdf | |
| 59 | +│ ├── 01_analysis.py # stage 1 (May 2026): RV construction → results/daily_rv_all.csv ; stages 3–8 superseded | |
| 60 | +│ ├── 02_connectedness_revision.py # stage 2 (Oct 2026): trading-day panel, log RV, VAR/GFEVD, bootstrap, robustness, rolling, regimes, yearly, Granger | |
| 61 | +│ └── 03_intraday_sessions.py # stage 3 (Oct 2026): ET→UTC conversion, hourly profile, session RV, session-ordered regressions | |
| 62 | +├── results/ # daily_rv_all.csv, table1_… (v1.0) ; rev_*.csv (v1.1) | |
| 63 | +├── figures/ # fig1…fig8 PNG (copied into paper/figures) | |
| 64 | +├── paper/ # main.tex + sections/ + appendix/ + tables/ (generated .tex) + references.bib → main.pdf | |
| 65 | +└── docs/ # REVIEW-REPORT.md, CHANGELOG-REVISION.md, main_pre-revision-20261017.pdf | |
| 61 | 66 | ``` |
| 62 | 67 | |
| 63 | 68 | ## 🚀 Quick start |
| 64 | 69 | |
| 65 | 70 | ```bash |
| 66 | 71 | python3 -m pip install -r requirements.txt |
| 67 | −# place the three DuckDB files in data/raw/ (or export WP6_DATA_DIR=/path/to/dbs) | |
| 68 | −python3 scripts/01_analysis.py # ≈ 10 min, ≈ 8 GB RAM (loads 235 M bars) | |
| 72 | +# optional stage 1: place the four DuckDB files in data/raw/ (or export WP6_DATA_DIR) — ≈ 10 min, ≈ 8 GB RAM | |
| 73 | +python3 scripts/01_analysis.py | |
| 74 | +# stage 2 (no raw data needed): all connectedness results, tables and figures 2–4, 6–8 — ≈ 1 min | |
| 75 | +python3 scripts/02_connectedness_revision.py | |
| 76 | +# stage 3: intraday sessions (export WP6_MINUTE_DIR=/path/to/1-min parquets) — ≈ 35 s | |
| 77 | +python3 scripts/03_intraday_sessions.py | |
| 69 | 78 | cd paper && make # latexmk → main.pdf |
| 70 | 79 | ``` |
| 71 | 80 | |
| 72 | 81 | ## 🗃 Data |
| 73 | 82 | |
| 74 | −5-minute OHLCV bars from FirstRate Data, 2008–2026: CME/CBOE continuous futures (ES, NQ, GC, CL, VX), spot FX (EURUSD, USDJPY, GBPUSD) and crypto spot (BTC, ETH). Realized volatility is the daily sum of squared 5-minute log returns; sessions are defined in exchange time. See `data/raw/README.md`. | |
| 83 | +5-minute OHLCV bars from FirstRate Data, 2008–2026, **time stamps in U.S. Eastern time**: continuous futures (ES, NQ, GC, CL), spot FX (EURUSD, USDJPY, GBPUSD), spot crypto (BTC, ETH, composite of exchanges) and the VIX index. Realized volatility is the daily sum of squared 5-minute log returns on Eastern-time calendar days (≥ 20 bars; returns beyond 20 sample s.d. dropped — a v1.0 choice disclosed in v1.1). The VAR panel is the set of trading days on which all ten instruments have an own RV (CBOE calendar, no forward filling). Intraday sessions use 1-minute bars of the same vendor converted to UTC. See `data/raw/README.md`. | |
| 75 | 84 | |
| 76 | 85 | ## 🔬 Methodology |
| 77 | 86 | |
| 78 | −1. **Realized volatility** per instrument and day from 5-minute closes (`scripts/01_analysis.py`, §1–2). | |
| 79 | −2. **Diebold–Yilmaz (2012) connectedness**: VAR(4) on log RV, generalized FEVD at H = 10, total / directional / net spillovers (§3). | |
| 80 | −3. **Rolling 200-day** windows for time variation (§4). | |
| 81 | −4. **Regime sub-samples**: pre-COVID, COVID crash, 2022 rate hikes (§5). | |
| 82 | −5. **Trading sessions**: hourly volatility profiles and session-level Granger causality (§6). | |
| 83 | −6. **Network graph** of net pairwise spillovers (§7). | |
| 87 | +1. **Realized volatility** per instrument and day (`01_analysis.py`), log-transformed for the VAR (ADF/KPSS reported). | |
| 88 | +2. **Diebold–Yilmaz (2012) connectedness**: VAR(4) (Hannan–Quinn), generalized FEVD at H = 10, TSI / TO / FROM / NET and net pairwise spillovers; **residual bootstrap** (B = 500) for 90 % intervals. | |
| 89 | +3. **Robustness grid**: levels vs log, p ∈ {1,2,3,6}, H ∈ {5,20}, weekend-inclusive crypto RV, sub-periods, exclusion of VIX / crypto. | |
| 90 | +4. **Rolling** windows of 200 / 250 / 500 trading days; **regimes** (4) and **calendar years** with intervals. | |
| 91 | +5. **Granger causality** (F and HAC Wald) on daily log RV. | |
| 92 | +6. **Sessions**: hourly profile in UTC, session RV shares, session-ordered predictive regressions, weekend-BTC → Monday-ES test. | |
| 84 | 93 | |
| 85 | 94 | ## 🖼 Figures & tables inventory |
| 86 | 95 | |
| 87 | 96 | | Figure | Content | |
| 88 | 97 | |---|---| |
| 89 | −| `fig1_rv_timeseries` | daily realized volatility, 10 instruments | | |
| 90 | −| `fig2_connectedness_heatmap` | full-sample spillover table | | |
| 91 | −| `fig3_rolling_spillover` | rolling total spillover index | | |
| 92 | −| `fig4_net_spillovers_regimes` | net spillovers by regime | | |
| 93 | −| `fig5_hourly_volatility` | intraday volatility by session | | |
| 94 | −| `fig6_net_directional_btc_es` | net directional spillovers BTC ↔ ES | | |
| 95 | −| `fig7_network_graph` | net pairwise spillover network | | |
| 98 | +| `fig1_rv_timeseries` | daily realized volatility, 10 instruments (v1.0) | | |
| 99 | +| `fig2_connectedness_heatmap` | full-sample GFEVD shares | | |
| 100 | +| `fig3_rolling_spillover` | rolling TSI, 200/250/500 trading days | | |
| 101 | +| `fig4_net_spillovers_regimes` | net spillovers by regime with 90 % intervals | | |
| 102 | +| `fig5_hourly_volatility` | hourly |5-min return| by UTC hour, ES/NQ/VIX/BTC | | |
| 103 | +| `fig6_net_directional_btc_es` | rolling net spillovers BTC and ES | | |
| 104 | +| `fig7_network_graph` | network of net pairwise spillovers | | |
| 105 | +| `fig8_yearly_crypto_integration` | BTC net spillover and exposure to traditional assets by year | | |
| 96 | 106 | |
| 97 | −Tables (`results/*.csv`): descriptive statistics, full connectedness table, three regime tables, session Granger tests. | |
| 107 | +Tables (`paper/tables/*.tex`, generated from `results/rev_*.csv`): RV descriptives, full connectedness with CIs, robustness grid, regimes (summary + 4 full matrices), calendar years, Granger, sessions, session-ordered regressions, weekend test, construction audit, lag selection, rolling summary. | |
| 98 | 108 | |
| 99 | 109 | ## ⚠️ Limitations |
| 100 | 110 | |
| 101 | −- Continuous futures series splice contracts at roll dates; roll returns are not removed. | |
| 102 | −- Crypto trades 24/7 while futures and FX have session gaps, so daily RV windows differ across classes. | |
| 103 | −- The GFEVD depends on the VAR lag (4) and horizon (10); robustness to these choices is reported in the appendix only. | |
| 111 | +- 5-minute returns beyond 20 s.d. were dropped before RV was computed (v1.0 pipeline; raw bars not available to re-run); composite crypto feed shows cross-venue price oscillations in 2017 (BTC RV > 1,000 % annualized on a few days — reproduced on the vendor's 1-minute feed). | |
| 112 | +- Continuous futures splice contracts at roll dates; roll returns are not removed. | |
| 113 | +- Linear, symmetric VAR; i.i.d. residual bootstrap (indicative intervals); 10 instruments, no fixed-income series. | |
| 114 | +- A "day" is an Eastern-time calendar day, which splits the Globex session; crypto weekend variance enters only in a robustness check. | |
| 104 | 115 | |
| 105 | 116 | ## 📝 Citation |
| 106 | 117 | |
| 107 | 118 | ```bibtex |
| 108 | 119 | @techreport{boucher2026connectedness, |
| 109 | 120 | author = {Boucher, Simon-Pierre}, |
| 110 | − title = {Intraday Volatility Transmission Across Asset Classes: A Connectedness Analysis of Equities, Fixed Income, Commodities, and Cryptocurrencies}, | |
| 121 | + title = {Intraday Volatility Transmission Across Asset Classes: A Connectedness Analysis of Equities, Foreign Exchange, Commodities, and Cryptocurrencies}, | |
| 111 | 122 | institution = {Universit\'e du Qu\'ebec en Outaouais, D\'epartement des sciences administratives}, |
| 112 | 123 | type = {Working Paper}, |
| 113 | 124 | number = {6}, |
| 114 | 125 | year = {2026}, |
| 115 | − month = {May} | |
| 126 | + month = {October}, | |
| 127 | + note = {Version 1.1} | |
| 116 | 128 | } |
| 117 | 129 | ``` |
| 118 | 130 | |
@@ -124,5 +136,7 @@ Université du Québec en Outaouais (UQO), Gatineau, QC. | ||
| 124 | 136 | |
| 125 | 137 | ## 🗒 Notes |
| 126 | 138 | |
| 127 | −- References are typeset with an inline `thebibliography` (`paper/sections/references.tex`, apalike style), not a `.bib` file — kept as is (deviation from `HARMONISATION.md` §3). | |
| 139 | +- **Revision 2026-10-17 (v1.0 → v1.1)**: scientific review by the editorial board — see `docs/REVIEW-REPORT.md` (diagnosis, verdicts, recommended analyses not executed, publication readiness) and `docs/CHANGELOG-REVISION.md` (audit trail of every correction, references verified/added/removed, re-analyses). Pre-revision state: git tag `pre-revision-20261017`, `docs/main_pre-revision-20261017.pdf`. | |
| 140 | +- Main corrections: trading-day panel instead of forward-filled calendar days; log RV; bootstrap intervals; Eastern→UTC time stamps in the intraday analysis; subtitle "Fixed Income" → "Foreign Exchange" (no fixed-income instrument in the sample); bibliography converted to `references.bib` (natbib/aer), 45 → 70 verified references. | |
| 141 | +- `results/table2…table4*.csv` and `rolling_total_spillover.csv` are the v1.0 outputs, kept for the audit; v1.1 outputs are prefixed `rev_`. | |
| 128 | 142 | - The original flat manuscript (`paper.tex`, May 2026) is archived in `Recherche-UQO/_archives/versions-mai-2026/intraday-volatility-connectedness--flat-tex-20260520/`. |
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| 1 | 1 | # Raw data — WP 6 |
| 2 | 2 | |
| 3 | −Three DuckDB databases of 5-minute OHLCV bars (2008–2026), each with a single table `ohlcv(symbol, datetime, open, high, low, close, volume)`: | |
| 3 | +## 5-minute bars (stage 1: `scripts/01_analysis.py`) | |
| 4 | + | |
| 5 | +Four DuckDB databases of 5-minute OHLCV bars (2008–2026), each with a single table `ohlcv(symbol, datetime, open, high, low, close, volume)`: | |
| 4 | 6 | |
| 5 | 7 | | File | Symbols used | Source | |
| 6 | 8 | |---|---|---| |
| 7 | −| `futures_5min.duckdb` | ES, NQ, GC, CL, VX (VIX futures) | FirstRate Data (CME/CBOE futures, continuous contracts) | | |
| 9 | +| `futures_5min.duckdb` | ES, NQ, GC, CL (continuous front-month futures; VX is present but not used) | FirstRate Data (CME/COMEX/NYMEX) | | |
| 8 | 10 | | `fx_5min.duckdb` | EURUSD, USDJPY, GBPUSD | FirstRate Data (spot FX) | |
| 9 | −| `crypto_5min.duckdb` | BTC, ETH | FirstRate Data (crypto spot, USD) | | |
| 11 | +| `crypto_5min.duckdb` | BTC, ETH | FirstRate Data (crypto spot, USD, composite of exchanges) | | |
| 12 | +| `index_5min.duckdb` | VIX | FirstRate Data (CBOE index, disseminated 03:15–16:15 ET; 09:30–16:15 before April 2016) | | |
| 13 | + | |
| 14 | +**Time stamps are naive U.S. Eastern time** (verified: Globex maintenance break at 17:00–18:00, VIX first bar at 03:15/09:30). A "day" in `results/daily_rv_all.csv` is therefore an Eastern-time calendar day. The May 2026 version of the paper read these stamps as UTC in its intraday analysis; the October 2026 revision converts them explicitly (`America/New_York` → UTC). | |
| 15 | + | |
| 16 | +The files total several GB and are **not committed**. Place them in this directory (or point `WP6_DATA_DIR` to their location) before running `scripts/01_analysis.py` (≈ 10 min, ≈ 8 GB RAM). The script keeps 5-minute log returns within 20 sample standard deviations of the mean, builds daily annualized realized volatility (≥ 20 bars per day) and writes `results/daily_rv_all.csv` and `results/table1_descriptive_stats.csv`. Known data feature: the composite crypto feed shows 5-minute price oscillations of 5–10 % between venues on several days of 2017 (BTC realized volatility above 1,000 % annualized on 2017-04-24/27, 2017-05-02/03, 2017-12-24); this is a property of the source, reproduced on the vendor's 1-minute feed. | |
| 17 | + | |
| 18 | +## 1-minute bars (stage 3: `scripts/03_intraday_sessions.py`) | |
| 19 | + | |
| 20 | +The intraday session analysis uses FirstRate 1-minute bars for ES, NQ, VIX and BTC held locally in the sibling repository `finance/realized-volatility-horse-race/data/raw/` (`futures_ES_1min.parquet`, `futures_NQ_1min.parquet`, `index_VIX_1min.parquet`, `crypto_BTC_1min.parquet`; 2013-01 → 2026-07, naive U.S. Eastern time stamps, not committed). Set `WP6_MINUTE_DIR` to their location. The script aggregates them to the paper's 5-minute grid over 2016-03-11 → 2026-03-11. | |
| 21 | + | |
| 22 | +## Stage 2 (`scripts/02_connectedness_revision.py`) | |
| 10 | 23 | |
| 11 | −The files total several GB and are **not committed**. Place them in this directory (or point `WP6_DATA_DIR` to their location) before running `scripts/01_analysis.py`. The script reads `SELECT datetime, close FROM ohlcv WHERE symbol = ?`, builds daily realized volatility from 5-minute log returns (≈ 235 million intraday observations across the 10 instruments) and writes everything to `results/` and `figures/`. | |
| 24 | +Needs only `results/daily_rv_all.csv` (committed): every VAR/GFEVD result of the paper can be reproduced without the raw bars. | |
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@@ -0,0 +1,139 @@ | ||
| 1 | +# Changelog — révision scientifique complète (editorial board, 2026-10-17) | |
| 2 | + | |
| 3 | +WP 6 — *Intraday Volatility Transmission Across Asset Classes* — version 1.0 (May 2026) → **1.1 (October 2026)**. | |
| 4 | +État avant révision : tag git `pre-revision-20261017`, PDF `docs/main_pre-revision-20261017.pdf` (31 p.). Après : `paper/main.pdf` (47 p.). | |
| 5 | +Rapport scientifique : `docs/REVIEW-REPORT.md`. | |
| 6 | + | |
| 7 | +Conventions : **Avant** = texte/chiffre de la v1.0 ; **Après** = v1.1 ; **Preuve** = fichier `results/` ou commande qui justifie la correction. | |
| 8 | + | |
| 9 | +--- | |
| 10 | + | |
| 11 | +## 1. Corrections majeures (données, méthode, chiffres) | |
| 12 | + | |
| 13 | +### 1.1 Panel du VAR : jours calendaires remplis par report → jours de bourse (CORRECTION CRITIQUE) | |
| 14 | +- **Où** : `scripts/01_analysis.py` §3 (`rv_panel.ffill(limit=5)` puis `dropna`), toutes les tables/figures de connectedness. | |
| 15 | +- **Avant** : panel de 3 651 jours calendaires (2016-03-11 → 2026-03-11) ; 1 044 lignes de fin de semaine et 1 137 lignes contenant au moins une valeur reportée (VIX, ES, FX, GC, CL figés sur leur valeur du vendredi/dimanche) ; sur > 30 % des observations, 8 des 10 séries avaient une innovation nulle par construction. La « fenêtre de 200 jours » couvrait 200 jours calendaires ≈ 143 jours de bourse. | |
| 16 | +- **Après** : panel des 2 514 jours de bourse où les 10 instruments ont une RV propre (calendrier CBOE), aucun report ; variante « weekend-inclusive » pour BTC/ETH en robustesse. | |
| 17 | +- **Preuve** : `results/rev_audit_construction.csv` — réplication exacte de l'original (TSI 55.44, ES +26.80, NQ +19.72, VIX −23.37, BTC +1.23) ; même panel sans report : TSI 50.04, ES +41.61 ; baseline révisée (log) : TSI 54.75. Script : `scripts/02_connectedness_revision.py` §1 et §4. | |
| 18 | +- **Conséquences** : isolement crypto surestimé (part propre BTC 79 % → 67 % ; part des actifs traditionnels dans la variance de BTC 1.3 % → 6.3 %) ; pic du TSI glissant de février 2018 (81.6 %) disparu (56.4 %). | |
| 19 | + | |
| 20 | +### 1.2 Variable du VAR : RV en niveaux → log RV | |
| 21 | +- **Avant** : VAR sur la volatilité réalisée annualisée (asymétrie 1.9–5.9, max BTC 1 409 % annualisé le 2017-04-27). | |
| 22 | +- **Après** : VAR sur ln σ (asymétrie 0.2–1.4), conformément à Andersen et al. (2003) ; niveaux conservés en robustesse (TSI 50.0 %). | |
| 23 | +- **Preuve** : `results/rev_table_rv_descriptives.csv`, `results/rev_table_robustness.csv` (ligne « RV in levels »). | |
| 24 | + | |
| 25 | +### 1.3 Inférence : aucune → bootstrap résiduel (B = 500 ; 300 par année civile), IC à 90 % | |
| 26 | +- **Preuve** : `results/rev_table_connectedness_full_ci.csv`, `rev_table_regimes.csv`, `rev_table_yearly.csv`. Référence : Kilian (1998), Kilian & Lütkepohl (2017). | |
| 27 | + | |
| 28 | +### 1.4 Fuseau horaire de l'analyse intrajournalière (CORRECTION CRITIQUE) | |
| 29 | +- **Où** : `01_analysis.py` §6 (commentaire « data is already UTC »), figure 5, §Trading session analysis, RQ5, abstract, conclusion. | |
| 30 | +- **Avant** : horodatages FirstRate lus comme UTC → « ES et NQ culminent pendant la session européenne (09:00–14:00 UTC) », « VIX culmine à 09:00–10:00 UTC ». | |
| 31 | +- **Après** : horodatages = heure de l'Est (vérifié : pause Globex 17:00–18:00 ET, ouverture VIX 03:15/09:30 ET) ; conversion America/New_York → UTC avec règles d'heure d'été. Les pics sont ceux de l'ouverture du cash américain (13:30–14:30 UTC) ; la session américaine génère 53 % (ES), 54 % (NQ), 63 % (VIX) de la variance quotidienne ; BTC : ratio pic/creux 1.2 (0.240 % à 07:00 UTC, 0.287 % à 18:00 UTC). | |
| 32 | +- **Preuve** : `scripts/03_intraday_sessions.py`, `results/rev_intraday_hourly_absret_utc.csv`, `rev_intraday_sessions.csv`, figure `fig5_hourly_volatility.png` régénérée à partir des barres 1 minute FirstRate du dépôt frère WP 12 (même fournisseur), agrégées à 5 minutes, 2016-03-11 → 2026-03-11. | |
| 33 | + | |
| 34 | +### 1.5 Tests de Granger « par session » fictifs | |
| 35 | +- **Avant** : `table4_session_granger.csv` répétait trois fois (Asian/European/US) les mêmes 9 tests sur la RV quotidienne ; le texte (RQ5) parlait de différences entre sessions. | |
| 36 | +- **Après** : (a) tests de Granger quotidiens sur log RV, 16 paires, F classique + Wald HAC (`rev_table_granger.csv`) ; (b) vraies régressions prédictives ordonnées par session (`rev_intraday_session_predictive.csv`) ; (c) test week-end BTC → lundi ES (`rev_intraday_weekend_btc_monday_es.csv`). | |
| 37 | + | |
| 38 | +### 1.6 Titre : « Fixed Income » → « Foreign Exchange » | |
| 39 | +- **Avant** : sous-titre « …Equities, Fixed Income, Commodities, and Cryptocurrencies » alors qu'aucun instrument de taux n'est dans l'échantillon (3 paires FX). | |
| 40 | +- **Après** : « …Equities, Foreign Exchange, Commodities, and Cryptocurrencies » (`\WPtitle`, `pdftitle`, README, citation BibTeX). Le titre court du standard (HARMONISATION §1) est inchangé. | |
| 41 | + | |
| 42 | +### 1.7 Nombre de bases de données et nature du VIX | |
| 43 | +- **Avant** : `data/raw/README.md` : « trois DuckDB », VIX = « VX (VIX futures) » ; papier : « quatre bases », VIX = indice ; intro RQ5 : « Bitcoin futures ». | |
| 44 | +- **Après** : quatre bases (`index_5min.duckdb` ajoutée au README), VIX = indice au comptant (RV des variations 5 min de l'indice), BTC/ETH = spot. Heures de cotation ajoutées à la table 1. | |
| 45 | + | |
| 46 | +### 1.8 Filtre à 20 écarts-types non divulgué | |
| 47 | +- **Avant** : `01_analysis.py` supprimait les rendements 5 min à plus de 20 σ avant le calcul de la RV ; non mentionné ; les bornes symétriques ±1.50 % (ES), ±1.70 % (NQ)… de la table 2 en sont la trace. | |
| 48 | +- **Après** : divulgué dans §Data et §Limitations ; effet non quantifiable sans retraiter les barres brutes (données brutes absentes du laptop). | |
| 49 | + | |
| 50 | +### 1.9 Artefacts de données crypto 2017 | |
| 51 | +- **Constat** : RV BTC > 1 000 % annualisée les 2017-04-24/27, 2017-05-02/03, 2017-12-24 (148 rendements 5 min > 5 % en une journée) ; reproduit sur le flux 1 minute indépendant du même fournisseur → propriété du flux composite (écarts de prix entre bourses), pas du traitement. | |
| 52 | +- **Après** : documenté dans §Data ; sous-échantillon 2018–2026 en robustesse (TSI 57.4, conclusions inchangées). | |
| 53 | + | |
| 54 | +### 1.10 Allégations non étayées retirées ou corrigées | |
| 55 | +| Allégation v1.0 | Statut v1.1 | Preuve | | |
| 56 | +|---|---|---| | |
| 57 | +| TSI glissant max 81.55 % le 2018-02-06, « précède Volmageddon », indicateur d'alerte précoce | Artefact (54.4 % le 02-02 → 56.4 % le 02-06) ; l'indice ne monte pas avant mars 2020 non plus ; interprétation « early warning » retirée | `rev_rolling_w200.csv`, `rev_key_numbers.csv` | | |
| 58 | +| USD/JPY +60.29 pp pendant la COVID, « ES bascule récepteur (−11.2) » | USD/JPY +81.8 [+7.3, +135.3] (signe établi, ampleur non) ; ES +19.4 [−23.3, +52.1] : pas de bascule établie ; T = 85, VAR(1) | `rev_table_regimes.csv` | | |
| 59 | +| BTC devient émetteur net en 2022 (+7.90) | −3.4 [−16.7, +12.4] : indiscernable de zéro ; en 2024–26 BTC récepteur net significatif −12.4 [−20.4, −2.1] | idem | | |
| 60 | +| Crypto « isolée » (part propre > 77 %, cross < 0.5 %) | part propre 65–67 % ; 6–7 % de la variance expliqués par les actifs traditionnels ; 46 % en 2025 | `rev_table_connectedness_full.csv`, `rev_table_yearly.csv` | | |
| 61 | +| « BTC causalement indépendant » (tous les tests BTC non significatifs) | BTC → VIX F = 5.1 (p < 0.001), BTC → ES p = 0.054 ; mais coefficients cumulés ≤ 0.03 ; 16 tests | `rev_table_granger.csv` | | |
| 62 | +| BTC net glissant « se stabilise à +4.58 % fin 2025 », ES « −0.62 % » | BTC −6.6 (moy. 2025, w = 200), −19.1 en mars 2026 (w = 500) ; ES +18 à +33 | `rev_rolling_w200.csv`, `rev_rolling_w500.csv` | | |
| 63 | +| « most comprehensive high-frequency multi-asset connectedness analysis to date » | retiré | — | | |
| 64 | + | |
| 65 | +### 1.11 Tables d'annexe de robustesse (lags, horizon) non produites par le script | |
| 66 | +- **Avant** : `appendix.tex` donnait des valeurs pour p ∈ {2, 6} et H ∈ {5, 20} qu'aucun script ne calculait. | |
| 67 | +- **Après** : grille complète calculée (`rev_table_robustness.csv`, 15 spécifications) ; valeurs originales remplacées. | |
| 68 | + | |
| 69 | +--- | |
| 70 | + | |
| 71 | +## 2. Chiffres modifiés (ancien → nouveau) | |
| 72 | + | |
| 73 | +| Objet | v1.0 | v1.1 | | |
| 74 | +|---|---|---| | |
| 75 | +| TSI plein échantillon | 55.44 % | 54.8 % [53.1, 56.9] | | |
| 76 | +| NET ES / NQ | +26.80 / +19.72 | +36.0 [29.9, 41.5] / +25.6 [19.0, 31.3] | | |
| 77 | +| NET VIX | −23.37 | −20.6 [−25.2, −14.0] | | |
| 78 | +| NET CL / GBPUSD / GC / USDJPY / EURUSD | −7.2 / −8.7 / −2.9 / −5.0 / +0.4 | −14.2 / −13.2 / −7.2 / −5.2 / −0.4 | | |
| 79 | +| NET BTC / ETH | +1.23 / −1.03 | +1.7 [−3.3, 6.4] / −2.4 [−7.9, 2.1] | | |
| 80 | +| Part propre BTC / ETH | 79.3 / 77.9 % | 66.7 / 64.9 % | | |
| 81 | +| BTC ↔ ETH | 19.3 / 20.6 % | 27.0 / 28.0 % | | |
| 82 | +| VIX ← ES / NQ | 15.0 / 13.2 % | 21.2 / 18.5 % | | |
| 83 | +| TSI glissant (200) : moyenne, min, max | 67.13, 57.22 (2020-09-26), 81.55 (2018-02-06) | 61.9, 50.5 (2017-10-27), 73.4 (2025-09-24) ; w = 500 : 58.3, 48.5, 66.5 | | |
| 84 | +| TSI régimes pré-COVID / COVID / 2022 | 64.72 / 66.66 / 65.62 | 59.9 / 71.7 / 64.6 (+ ETF 65.5) | | |
| 85 | +| NET ES pré-COVID | +76.4 | +41.3 [23.0, 55.6] | | |
| 86 | +| Granger ES → VIX | F = 19.864 (niveaux, 2013–2026) | F = 19.94, Wald HAC 62.8 (log, 2016–2026) | | |
| 87 | +| Session la plus volatile ES/NQ | « européenne » | américaine (53–54 % de la variance) | | |
| 88 | +| Profil BTC | « uniforme 0.24–0.27 % » | 0.240–0.287 %, pic/creux 1.2, bosse en heures US | | |
| 89 | +| Nb de références | 45 | 70 | | |
| 90 | +| Pages | 31 | 47 | | |
| 91 | + | |
| 92 | +Les moyennes de RV annualisée (§Data) passent de la pleine histoire (ES 13.85 %) au panel commun 2016–2026 (ES 13.9 %) ; la table 2 (rendements 5 min) est inchangée faute de données brutes. | |
| 93 | + | |
| 94 | +--- | |
| 95 | + | |
| 96 | +## 3. Réanalyses exécutées | |
| 97 | + | |
| 98 | +| Script | Entrée | Durée | Sorties | | |
| 99 | +|---|---|---|---| | |
| 100 | +| `scripts/02_connectedness_revision.py` | `results/daily_rv_all.csv` | ≈ 70 s | `results/rev_*.csv` (descriptives, audit, plein échantillon + IC, robustesse 15 spéc., rolling w = 200/250/500, 4 régimes + IC, années civiles + IC, Granger, critères de retard, clés) ; `paper/tables/tab_*.tex` ; `figures/fig2,3,4,6,7,8` | | |
| 101 | +| `scripts/03_intraday_sessions.py` | barres 1 min FirstRate (ES, NQ, VIX, BTC) du dépôt frère `finance/realized-volatility-horse-race/data/raw/` (`WP6_MINUTE_DIR`) | ≈ 35 s | `results/rev_intraday_*.csv`, `paper/tables/tab_sessions*.tex`, `tab_weekend_btc.tex`, `figures/fig5_hourly_volatility.png` | | |
| 102 | +| Vérification croisée RV BTC 2017 | idem (1 min → 5 min) | < 10 s | 2017-04-27 : 14.04 (vs 14.09 dans `daily_rv_all.csv`) | | |
| 103 | + | |
| 104 | +Non exécuté : `01_analysis.py` (bases DuckDB 5 min absentes du laptop) — `daily_rv_all.csv` et `table1_descriptive_stats.csv` d'origine réutilisés ; fig. 1 conservée. | |
| 105 | + | |
| 106 | +--- | |
| 107 | + | |
| 108 | +## 4. Références | |
| 109 | + | |
| 110 | +### 4.1 Vérification (45 entrées v1.0, Crossref 2026-10-17, DOI de revue inscrit dans `references.bib`) | |
| 111 | +- 39 entrées exactes (données bibliographiques confirmées, DOI ajouté). | |
| 112 | +- Corrigées : **Eross et al. (2019)** — auteurs « Kallinterakis, Tong » → Eross, McGroarty, Urquhart, Wolfe ; **Bouri et al.** QREF 77 → année 2020 (clé `Bouri2020`) ; **Yousaf et al.** JIFMIM 82 → 2023 ; **« Diebold & Yilmaz (2012b) » Trans-Atlantic** → JFEC 14(1), 2016 (`DieboldYilmaz2016`) ; Mandelbrot 1963 pages 394–419 ; Fama 1965 pages 34–105 ; Granger 1969 pages 424–438. | |
| 113 | +- Retirées (contenu cité ne correspondait pas à l'article) : **Ante (2021)** (article de 2023 sur les tweets d'Elon Musk, cité pour l'adoption institutionnelle) ; **Fry & Cheah (2022)** (IRFA 47 est de 2016, « negative bubbles », cité pour le canal d'information 24/7) ; **Greenwood-Nimmo, Nguyen & Shin (2014)** (connectedness macro mondiale, IJF 2021 ; cité pour le carry trade → actions). | |
| 114 | +- Attributions de contenu corrigées dans le texte : Barunik–Kocenda–Vacha 2016 (actions US, pas EUR/USD) ; Kang et al. 2017 (pétrole–métaux–agricoles, pas actions) ; Vivian & Wohar 2012 (ruptures, pas spillovers pétrole–actions) ; Reboredo 2013 (or–dollar, pas or–pétrole) ; Bouri et al. 2020 (safe haven ondelettes, pas « connectedness accrue après 2017 ») ; Yousaf et al. 2023 (meme assets). | |
| 115 | + | |
| 116 | +### 4.2 Ajoutées (28, toutes vérifiées Crossref/DOI résolu) | |
| 117 | +Andersen & Bollerslev 1997 JEF (10.1016/S0927-5398(97)00004-2) ; Andersen, Bollerslev & Diebold 2007 REStat (10.1162/rest.89.4.701) ; Aït-Sahalia, Mykland & Zhang 2005 RFS (10.1093/rfs/hhi016) ; Bollerslev, Patton & Quaedvlieg 2016 JoE (10.1016/j.jeconom.2015.10.007) ; Corsi 2009 JFEC (10.1093/jjfinec/nbp001) ; Hansen & Lunde 2006 JBES (10.1198/073500106000000071) ; Baruník, Kočenda & Vácha 2017 JIMF (10.1016/j.jimonfin.2017.06.003) ; Diebold & Yilmaz 2016 JFEC (10.1093/jjfinec/nbv021) ; Greenwood-Nimmo, Nguyen & Rafferty 2016 JFM (10.1016/j.finmar.2016.05.001) ; Lastrapes & Wiesen 2021 Econ. Modelling (10.1016/j.econmod.2020.02.010) ; Dickey & Fuller 1979 JASA (10.2307/2286348) ; Kwiatkowski et al. 1992 JoE (10.1016/0304-4076(92)90104-Y) ; Newey & West 1987 Econometrica (10.2307/1913610) ; Kilian 1998 REStat (10.1162/003465398557465) ; Kilian & Lütkepohl 2017 CUP (10.1017/9781108164818) ; Lütkepohl 2005 Springer (10.1007/978-3-540-27752-1) ; Arouri, Jouini & Nguyen 2011 JIMF (10.1016/j.jimonfin.2011.07.008) ; Mensi et al. 2013 Econ. Modelling (10.1016/j.econmod.2013.01.023) ; Bekaert & Hoerova 2014 JoE (10.1016/j.jeconom.2014.05.008) ; Whaley 2009 JPM (10.3905/jpm.2009.35.3.098) ; Baur, Hong & Lee 2018 JIFMIM (10.1016/j.intfin.2017.12.004) ; Baur et al. 2019 FRL (10.1016/j.frl.2019.04.023) ; Chaim & Laurini 2018 Econ. Letters (10.1016/j.econlet.2018.10.011) ; Katsiampa 2017 Econ. Letters (10.1016/j.econlet.2017.06.023) ; Conlon & McGee 2020 FRL (10.1016/j.frl.2020.101607) ; Elsayed, Gozgor & Lau 2022 IRFA (10.1016/j.irfa.2022.102069) ; Iyer 2022 IMF GFS Note (10.5089/9781616358068.065) ; Ji, Bouri, Lau & Roubaud 2019 IRFA (10.1016/j.irfa.2018.12.002) ; Ji, Bouri, Roubaud & Kristoufek 2019 Energy Econ. (10.1016/j.eneco.2019.06.005). | |
| 118 | +- Écartée après vérification : Corbet, Lucey, Urquhart & Yarovaya 2019 IRFA — **rétractée** selon Crossref. | |
| 119 | + | |
| 120 | +### 4.3 Format | |
| 121 | +`sections/references.tex` (`thebibliography`, apalike) → `paper/references.bib` + natbib `[authoryear,round,semicolon]` + `\bibliographystyle{aer}` ; 70 entrées, 70 citées, 0 citation indéfinie. | |
| 122 | + | |
| 123 | +--- | |
| 124 | + | |
| 125 | +## 5. Forme et LaTeX | |
| 126 | +- `\WPversion` 1.0 → 1.1 ; `\WPdate` May 2026 → October 2026 ; abstract, mots-clés et JEL (G17 retiré : aucune prévision) réécrits dans `main.tex`. | |
| 127 | +- Toutes les tables de résultats sont des fragments générés (`paper/tables/*.tex`, `\input`) ; aucune valeur tapée à la main sauf la table 2 (rendements 5 min) reprise de `table1_descriptive_stats.csv`. | |
| 128 | +- Listes à puces du corps (RQ, épisodes) converties en prose ; superlatifs retirés ; « % » → « percentage points » pour les NET. | |
| 129 | +- Nouvelles figures : fig. 8 (intégration crypto par année) ; fig. 2, 3, 4, 5, 6, 7 régénérées ; fig. 1 conservée. | |
| 130 | +- Annexe : audit de la construction du panel, critères de retard, résumé des fenêtres glissantes, 4 matrices complètes de régime, note de réplication. | |
| 131 | +- `cd paper && make` : 0 erreur, 0 citation/référence indéfinie. `titlepage.tex` intact. | |
| 132 | + | |
| 133 | +## 6. Code | |
| 134 | +- `scripts/01_analysis.py` : inchangé dans sa logique (seule source de `daily_rv_all.csv`) ; en-tête ajouté signalant que ses sections 3–8 sont remplacées par `02_` et `03_` et listant les défauts connus (report des fins de semaine, fuseau, Granger « par session », filtre 20 σ). | |
| 135 | +- `data/raw/README.md` : quatre bases, fuseau horaire, origine des barres 1 min utilisées par `03_`. | |
| 136 | +- Les sorties v1.0 (`table2_…`, `table3*_…`, `table4_session_granger.csv`, `rolling_total_spillover.csv`) sont conservées pour l'audit ; les sorties v1.1 sont préfixées `rev_`. | |
| 137 | + | |
| 138 | +## 7. Non modifié faute de données | |
| 139 | +- Table 2 (statistiques des rendements 5 min) et fig. 1 ; effet du filtre 20 σ ; retrait des rendements de roulement des futures ; estimateurs robustes aux sauts (bipower) ; RV crypto sur une seule bourse. | |
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docs/REVIEW-REPORT.md
+109 −0
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| 1 | +# Rapport de l'« editorial board » — WP 6 (révision du 2026-10-17) | |
| 2 | + | |
| 3 | +**Papier** : *Intraday Volatility Transmission Across Asset Classes: A Connectedness Analysis of Equities, Foreign Exchange, Commodities, and Cryptocurrencies* — UQO Working Paper No. 6, v1.0 (May 2026) → v1.1 (October 2026). | |
| 4 | +**Comité** : volatilité réalisée, connectedness (Diebold–Yilmaz), économétrie des séries temporelles, marchés crypto, microstructure. | |
| 5 | +**Revues de référence** : Journal of Econometrics, JFEC, JBF, Journal of Financial Markets, IRFA, Journal of Empirical Finance, Energy Economics. | |
| 6 | +**Matériel examiné** : README, `paper/main.tex` + 8 sections + annexe (31 p.), `references.tex` (45 entrées), `scripts/01_analysis.py`, `results/*.csv`, 7 figures, `data/raw/README.md` ; données brutes 5 min absentes du laptop, `daily_rv_all.csv` (6 367 jours × 10) présent, barres 1 min FirstRate du WP 12 présentes. | |
| 7 | +**Journal des corrections** : `docs/CHANGELOG-REVISION.md`. | |
| 8 | + | |
| 9 | +--- | |
| 10 | + | |
| 11 | +## 1. Diagnostic général | |
| 12 | + | |
| 13 | +La v1.0 posait une question pertinente (hiérarchie de transmission de la volatilité réalisée entre quatre classes d'actifs, 2016–2026, avec crypto) et appliquait un cadre standard (GFEVD d'un VAR(4), H = 10). Elle souffrait de **quatre défauts de construction** qui invalidaient une partie substantielle des conclusions : | |
| 14 | + | |
| 15 | +1. **Panel du VAR sur jours calendaires avec report (`ffill`)** : 3 651 lignes dont 1 044 week-ends et 1 137 lignes avec au moins une valeur figée ; 8 séries sur 10 avaient une innovation nulle sur > 30 % des observations. Effet : isolement crypto surestimé, NET des futures actions comprimé de 15 pp, pic « Volmageddon » de février 2018 (81.6 %) purement artificiel, fenêtre « 200 jours » = 143 jours de bourse. | |
| 16 | +2. **VAR sur RV en niveaux** avec des journées à 1 400 % annualisé (artefacts du flux crypto composite de 2017) qui dominent la matrice de covariance. | |
| 17 | +3. **Fuseau horaire** : horodatages FirstRate (heure de l'Est) lus comme UTC → les pics de volatilité d'ES/NQ/VIX attribués à la « session européenne » étaient l'ouverture du cash américain décalée de 4–5 h ; RQ5, abstract, résultats et conclusion erronés sur ce point. | |
| 18 | +4. **Aucune inférence** : conclusions de régime (USD/JPY émetteur dominant en COVID, ES « bascule » récepteur, BTC « devient émetteur » en 2022) tirées de VAR(4) à 41 paramètres/équation sur 85–290 observations, sans intervalle de confiance. | |
| 19 | + | |
| 20 | +S'y ajoutaient : un titre annonçant du « Fixed Income » sans aucun instrument de taux ; des tests de Granger « par session » qui répétaient trois fois le même test quotidien ; des tables de robustesse d'annexe sans script source ; un filtre à 20 σ non divulgué ; une bibliographie en `thebibliography` avec 3 références dont le contenu cité ne correspondait pas à l'article et plusieurs erreurs bibliographiques. | |
| 21 | + | |
| 22 | +Le point positif : `daily_rv_all.csv` (pré-report) était versionné, ce qui a permis de **refaire intégralement** l'étape VAR/GFEVD, et des barres 1 min du même fournisseur étaient disponibles localement, ce qui a permis de refaire l'analyse intrajournalière avec le bon fuseau. Toutes les réanalyses tiennent en moins de deux minutes. | |
| 23 | + | |
| 24 | +--- | |
| 25 | + | |
| 26 | +## 2. Diagnostic par section (v1.0 → v1.1) | |
| 27 | + | |
| 28 | +| Section | Forces | Faiblesses / erreurs trouvées | Traitement | | |
| 29 | +|---|---|---|---| | |
| 30 | +| Abstract | chiffres précis | « Fixed Income » ; « intraday transmission at the 5-minute frequency » (le VAR est quotidien) ; résultats faux (session européenne, BTC émetteur 2022, isolement crypto, pic 2018) ; G17 (prévision) injustifié | réécrit ; IC ajoutés ; direction equities → crypto ; JEL G17 retiré | | |
| 31 | +| Introduction | motivation claire | 5 RQ dont RQ4 (« early warning ») contredite par les propres données ; RQ5 mentionne « Bitcoin futures » (spot) ; « novel », « most comprehensive » ; listes à puces | RQ reformulées en prose ; contribution recentrée (alignement calendaire, inférence, sessions) ; paragraphe signalant la révision | | |
| 32 | +| Littérature | couverture classique correcte | 6 attributions de contenu erronées (Barunik 2016 « EUR/USD », Kang 2017 « actions », Vivian 2012 « pétrole–actions », Reboredo « or–pétrole », Bouri 2019 « connectedness post-2017 », Greenwood-Nimmo « carry trade ») ; Ante 2021 et Fry & Cheah 2022 hors sujet ; Eross et al. mauvais auteurs ; rien sur l'inférence, le long memory, le fuseau/calendrier, l'IMF 2022 | 3 retraits, 28 ajouts vérifiés, sous-section VIX (RV de l'indice ≠ niveau), sous-section RV/périodicité | | |
| 33 | +| Méthodologie | équations GFEVD/TSI correctes | pas de justification du log ; p = 4 « throughout » sans critère ; pas d'inférence ; F de Granger sans HAC ; réseau défini sur θ brut et non sur les spillovers nets par paire ; aucune équation pour l'analyse de session | log RV + ADF/KPSS ; critères AIC/BIC/HQ (3/4/5) ; bootstrap résiduel (Kilian 1998) ; Wald HAC ; NET par paire (eq. 10) ; eq. 15–16 pour les sessions ; discussion de la sur-paramétrisation des fenêtres courtes | | |
| 34 | +| Données | table d'univers, stats 5 min | « four databases » vs README « three » ; heures de cotation absentes ; aucune section sur l'alignement temporel ; filtre 20 σ caché ; moyennes RV sur pleine histoire alors que le VAR porte sur 2016–2026 ; artefacts 2017 non signalés | §Time stamps and alignment (nouvelle) ; table 1 avec heures ; table RV du panel commun (moments, ρ1, ADF, KPSS) ; divulgation du filtre ; vérification croisée des artefacts | | |
| 35 | +| Résultats | tables complètes | voir §1 ; « 190.4 % of directional spillovers » (somme de TO, sans sens) ; épisodes décrits à partir d'artefacts ; valeurs NET en « % » | 8 sous-sections régénérées, IC partout, grille de robustesse, 3 fenêtres, 4 régimes, années civiles, Granger HAC, sessions UTC, régressions ordonnées, test week-end | | |
| 36 | +| Discussion | structure par RQ | affirmations non étayées (early warning, bascules de signe) | réponses recalibrées, leçons méthodologiques, limites élargies | | |
| 37 | +| Conclusion | — | reprend les erreurs | réécrite, extensions ciblées | | |
| 38 | +| Annexe | — | tables p ∈ {2,6}, H ∈ {5,20} sans source ; « Summary of key findings » redondant | audit de la construction, critères de retard, résumé rolling, 4 matrices de régime, réplication | | |
| 39 | + | |
| 40 | +--- | |
| 41 | + | |
| 42 | +## 3. Méthodologie — verdict motivé (master prompt §3) | |
| 43 | + | |
| 44 | +| Point | Verdict | Motif | | |
| 45 | +|---|---|---| | |
| 46 | +| Spécification justifiée | **Oui (v1.1)** | VAR(4) = choix HQ ; p ∈ {1,2,3,6} et H ∈ {5,20} en robustesse ; TSI stable 53.7–55.5 % | | |
| 47 | +| Hypothèses d'estimation explicites | Oui | stationnarité testée (ADF rejette la racine unitaire ; KPSS rejette la stationnarité de niveau → long memory, approximation VAR notée) ; bootstrap i.i.d. explicitement limité | | |
| 48 | +| Variables correctement définies | Oui | RV, σ annualisée, log σ, RV de session ; VIX = RV des variations de l'indice (clarifié) | | |
| 49 | +| Dépendance temporelle | Défendable | HAC (Newey–West 10 retards) pour Granger et régressions de session ; bootstrap résiduel pour le GFEVD | | |
| 50 | +| Écarts-types | Oui | IC 90 % bootstrap sur TSI/TO/FROM/NET ; HAC sur régressions | | |
| 51 | +| Construction de l'échantillon transparente | Oui | 2 514 jours de bourse, aucun report ; audit de la construction v1.0 en annexe | | |
| 52 | +| Robustesse ciblant de vraies menaces | Oui | niveaux vs log ; p, H ; week-end crypto ; 2018+ ; sous-périodes ; exclusion VIX/crypto/ETH ; fenêtres 200/250/500 | | |
| 53 | +| Interprétation des coefficients | Corrigée | NET en pp ; TO peut dépasser 100 ; « 190 % » retiré ; somme des coefficients Granger rapportée | | |
| 54 | +| Significativité statistique vs économique | Oui | Granger : effets détectables mais coefficients cumulés ≤ 0.07 et 16 tests ; sessions : ΔR² reportés | | |
| 55 | +| Affirmations causales | Encadrées | « Granger-cause », « predicts », « net receiver » ; aucune causalité structurelle revendiquée | | |
| 56 | + | |
| 57 | +--- | |
| 58 | + | |
| 59 | +## 4. Littérature | |
| 60 | + | |
| 61 | +- **Vérifiées** : 45/45 entrées v1.0 passées à Crossref ; DOI de revue inscrits ; 3 retirées (contenu non conforme), 7 corrigées (auteurs, année, pages), 6 attributions textuelles corrigées. Détail dans le changelog §4. | |
| 62 | +- **Ajoutées** : 28 références (DOI résolus), intégrées à l'argument : mesure de RV et bruit de microstructure (Hansen & Lunde 2006 ; Aït-Sahalia et al. 2005 ; Andersen et al. 2007 ; Corsi 2009 ; Bollerslev et al. 2016), connectedness FX/commodités (Baruník et al. 2017 ; Greenwood-Nimmo et al. 2016 ; Arouri et al. 2011 ; Mensi et al. 2013 ; Lastrapes & Wiesen 2021 ; Diebold & Yilmaz 2016), VIX (Whaley 2009 ; Bekaert & Hoerova 2014), crypto (Baur et al. 2018, 2019 ; Katsiampa 2017 ; Chaim & Laurini 2018 ; Conlon & McGee 2020 ; Elsayed et al. 2022 ; Iyer 2022 ; Ji et al. 2019a,b), inférence et séries (Kilian 1998 ; Kilian & Lütkepohl 2017 ; Lütkepohl 2005 ; Dickey & Fuller 1979 ; KPSS 1992 ; Newey & West 1987 ; Andersen & Bollerslev 1997). | |
| 63 | +- **Écartée** : Corbet, Lucey, Urquhart & Yarovaya (2019, IRFA) — rétractée. | |
| 64 | +- Total : 45 → **70** références, format `.bib` + natbib/aer, 0 citation indéfinie. | |
| 65 | + | |
| 66 | +--- | |
| 67 | + | |
| 68 | +## 5. Résultats — incohérences trouvées et état après révision | |
| 69 | + | |
| 70 | +1. Abstract/intro/README : « 2008–2026 » pour le VAR alors que le panel commun commence en mars 2016 → distinction explicite (données 2008–2026, VAR 2016–2026). | |
| 71 | +2. Table 2 vs texte : Kurt = excès de kurtosis (scipy) — cohérent ; bornes ±1.5 % = filtre 20 σ → divulgué. | |
| 72 | +3. TSI glissant 57.22–81.55 % vs plein échantillon 55.44 % : biais de sur-paramétrisation + artefact de calendrier → expliqué ; w = 500 donne 58.3 % de moyenne. | |
| 73 | +4. « ES flips to receiver » (COVID, −11.2) : sur panel correct, +19.4 [−23.3, +52.1] → retiré. | |
| 74 | +5. BTC +7.9 en 2022 : −3.4 [−16.7, +12.4] → retiré ; BTC −12.4 [−20.4, −2.1] en 2024–26 → nouveau résultat. | |
| 75 | +6. « crypto causally independent » : BTC → VIX significatif, mais économiquement faible → nuancé. | |
| 76 | +7. Granger « par session » identique sur 3 sessions → remplacé. | |
| 77 | +8. Fig. 5 étiquetée UTC alors qu'en heure de l'Est → régénérée. | |
| 78 | +9. Appendix p/H robustesse sans source → recalculée. | |
| 79 | +10. Moyennes RV du §Data (pleine histoire) vs panel VAR → table dédiée au panel commun. | |
| 80 | + | |
| 81 | +--- | |
| 82 | + | |
| 83 | +## 6. Réanalyses exécutées (toutes versionnées) | |
| 84 | + | |
| 85 | +- `scripts/02_connectedness_revision.py` (≈ 70 s) : panel jours de bourse, log RV, VAR(4)/H = 10, bootstrap B = 500, grille de robustesse (15 spéc.), rolling w = 200/250/500, 4 régimes + IC, années civiles + IC (B = 300), Granger F + Wald HAC (16 paires), critères de retard, réplication exacte de la v1.0, 6 figures, 11 fragments LaTeX. | |
| 86 | +- `scripts/03_intraday_sessions.py` (≈ 35 s) : barres 1 min FirstRate (WP 12) → 5 min, conversion America/New_York → UTC, profil horaire, RV de session, parts de variance, régressions prédictives ordonnées (11), test week-end BTC → lundi ES, part de variance du week-end, 3 fragments LaTeX, fig. 5. | |
| 87 | + | |
| 88 | +## 7. Analyses recommandées **non exécutées** | |
| 89 | + | |
| 90 | +| Analyse | Raison | Priorité | | |
| 91 | +|---|---|---| | |
| 92 | +| Recalcul de la RV sans le filtre 20 σ, avec bipower variation (Andersen et al. 2007) et RV crypto sur une seule bourse | bases DuckDB 5 min absentes du laptop ; pipeline 01 non relançable | haute | | |
| 93 | +| Retrait des rendements de roulement des futures continus | idem | moyenne | | |
| 94 | +| TVP-VAR (Antonakakis et al. 2020) ou VAR avec shrinkage pour les fenêtres courtes | hors périmètre temps ; recommandé pour formaliser la rupture 2020 | haute | | |
| 95 | +| Connectedness fréquentielle (Baruník & Křehlík 2018) | extension | moyenne | | |
| 96 | +| Bootstrap par blocs ou wild bootstrap tenant compte de l'hétéroscédasticité conditionnelle | l'IC résiduel i.i.d. est indicatif | moyenne | | |
| 97 | +| Test de rupture formel (sup-Wald / Bai–Perron) sur l'intégration crypto | les IC annuels suffisent à montrer le changement, pas à le dater | moyenne | | |
| 98 | +| Connectedness asymétrique (bonne/mauvaise volatilité) | extension | basse | | |
| 99 | +| Élargissement du système (ZN/TLT, AUD, agricoles, altcoins) ; ZN 1 min disponible dans WP 12 | changerait le papier (titre « Fixed Income » redeviendrait pertinent) | moyenne | | |
| 100 | + | |
| 101 | +## 8. Limites restantes | |
| 102 | +Filtre 20 σ en amont ; artefacts du flux crypto 2016–2017 ; roulements de futures ; VAR linéaire symétrique ; bootstrap i.i.d. ; 10 instruments (pas de taux) ; « jour » = jour calendaire de l'Est (coupe la session Globex) ; VIX = RV d'un indice non négociable. | |
| 103 | + | |
| 104 | +## 9. Maturité pour publication | |
| 105 | + | |
| 106 | +- **État** : manuscrit cohérent, reproductible (3 scripts, tables générées), avec inférence ; les conclusions sont désormais défendables et plus modestes que la v1.0. | |
| 107 | +- **Revue cible réaliste** : *International Review of Financial Analysis* ou *Journal of International Financial Markets, Institutions and Money* (contribution empirique + leçon méthodologique sur l'alignement calendaire) ; *Finance Research Letters* pour une version courte centrée sur crypto. *Journal of Financial Econometrics* / *Journal of Econometrics* improbables sans contribution méthodologique (inférence sur GFEVD, TVP) ; *Energy Economics* seulement si recentré sur CL/GC. | |
| 108 | +- **Risques de rejet** : (i) cadre DY standard sans innovation méthodologique ; (ii) filtre 20 σ et données crypto composites (un arbitre demandera le recalcul) ; (iii) absence d'instrument de taux dans un papier « cross-asset » ; (iv) bootstrap i.i.d. ; (v) le résultat principal sur la crypto (récepteur net, intégration croissante) rejoint Iyer (2022) — la valeur ajoutée est la mesure RV, les sessions et la démonstration de sensibilité au calendrier, qu'il faut mettre en avant. | |
| 109 | +- **Verdict** : *major revision done* au sens d'un comité interne ; soumission possible après (a) recalcul de la RV sans filtre et avec RV crypto mono-bourse, (b) ajout d'un TVP-VAR ou d'un test de rupture formel. | |
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paper/appendix/appendix.tex
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@@ -1,97 +1,99 @@ | ||
| 1 | −\section{Robustness Checks} | |
| 2 | −\label{sec:robustness} | |
| 1 | +\section{Audit of the Panel Construction} | |
| 2 | +\label{sec:appendix_audit} | |
| 3 | 3 | |
| 4 | −\subsection{Sensitivity to VAR Lag Selection} | |
| 4 | +\Cref{tab:audit_construction} reproduces the full-sample estimates of the May 2026 version of this paper and traces the effect of the two corrections made in the present version. The first row replicates the original computation exactly from the archived daily realized-volatility file: a panel of all 3{,}651 calendar days between 11 March 2016 and 11 March 2026, with missing values forward-filled for up to five days and realized volatility in levels. The second row removes the forward filling and the weekend rows, leaving the 2{,}514 trading days on which all ten instruments have an own realized volatility. The third row applies the log transformation to that panel and is the baseline of \Cref{sec:results}. | |
| 5 | 5 | |
| 6 | −We verify robustness to alternative VAR lag specifications. \Cref{tab:robustness_lags} reports the total spillover index and top-3 net transmitters for $p \in \{2, 4, 6\}$. | |
| 6 | +\begin{table}[htbp] | |
| 7 | +\centering | |
| 8 | +\caption{Effect of the panel construction on full-sample connectedness, VAR(4), $H = 10$.} | |
| 9 | +\label{tab:audit_construction} | |
| 10 | +\adjustbox{max width=\textwidth}{% | |
| 11 | +\begin{threeparttable} | |
| 12 | +\input{tables/tab_audit_construction} | |
| 13 | +\begin{tablenotes}[flushleft] | |
| 14 | +\footnotesize | |
| 15 | +\item \textit{Notes:} TSI in percent; the other columns are net directional spillovers in percentage points. The first row reproduces the published figures of the May 2026 version (TSI 55.44\%, ES $+26.80$, NQ $+19.72$, VIX $-23.37$, BTC $+1.23$). Of the 3{,}651 rows of the original panel, 1{,}044 were Saturdays or Sundays and 1{,}137 contained at least one forward-filled value. Source: \path{results/rev_audit_construction.csv}. | |
| 16 | +\end{tablenotes} | |
| 17 | +\end{threeparttable}} | |
| 18 | +\end{table} | |
| 19 | + | |
| 20 | +The forward filling lowers the total index by about five percentage points relative to the trading-day panel in levels (55.4\% against 50.0\%) while compressing the net spillover of ES from $+41.6$ to $+26.8$ and of NQ from $+29.8$ to $+19.7$; the near-coincidence of the original index (55.4\%) with the revised baseline (54.8\%) is the result of two offsetting changes, forward filling and the log transformation, and not of robustness. The forward-filled panel also drove the own shares of bitcoin and ether above 77\% and their cross-asset shares below 0.5\%, because on weekend rows the innovations of the eight traditional series are identically zero while those of the cryptocurrencies are not. In the rolling analysis, the original 200-observation window covered 200 calendar days, or about 143 trading days, and the index reached 81.5\% on 6 February 2018 against 56.4\% on the trading-day panel (\Cref{tab:rolling_summary}). | |
| 7 | 21 | |
| 8 | 22 | \begin{table}[htbp] |
| 9 | 23 | \centering |
| 10 | −\caption{Robustness to VAR Lag Selection.} | |
| 11 | −\label{tab:robustness_lags} | |
| 24 | +\caption{Summary of rolling total spillover indices.} | |
| 25 | +\label{tab:rolling_summary} | |
| 26 | +\adjustbox{max width=\textwidth}{% | |
| 12 | 27 | \begin{threeparttable} |
| 13 | −\begin{tabular}{@{}lrrr@{}} | |
| 14 | −\toprule | |
| 15 | −& $p=2$ & $p=4$ (baseline) & $p=6$ \\ | |
| 16 | −\midrule | |
| 17 | −Total Spillover Index (\%) & 53.8 & 55.4 & 56.9 \\ | |
| 18 | −ES net spillover (\%) & $+$25.1 & $+$26.8 & $+$27.4 \\ | |
| 19 | −NQ net spillover (\%) & $+$18.3 & $+$19.7 & $+$20.5 \\ | |
| 20 | −VIX net spillover (\%) & $-$21.8 & $-$23.4 & $-$24.1 \\ | |
| 21 | −\bottomrule | |
| 22 | −\end{tabular} | |
| 28 | +\input{tables/tab_rolling_summary} | |
| 23 | 29 | \begin{tablenotes}[flushleft] |
| 24 | 30 | \footnotesize |
| 25 | −\item \textit{Notes:} Total spillover index and selected net directional spillovers under alternative VAR lag orders. Directional rankings remain qualitatively unchanged across all specifications. | |
| 31 | +\item \textit{Notes:} Mean, minimum and maximum of the rolling total spillover index (\%) with the dates at which the extremes occur. The first row is the series published in the May 2026 version; the others are VAR(4), $H = 10$ estimates on log realized volatility over the trading-day panel. Source: \path{results/rev_rolling_summary.csv}. | |
| 26 | 32 | \end{tablenotes} |
| 27 | −\end{threeparttable} | |
| 33 | +\end{threeparttable}} | |
| 28 | 34 | \end{table} |
| 29 | 35 | |
| 30 | −\subsection{Sensitivity to Forecast Horizon} | |
| 36 | +\section{Lag-Order Selection} | |
| 37 | +\label{sec:appendix_lags} | |
| 31 | 38 | |
| 32 | −\Cref{tab:robustness_horizon} reports sensitivity to the forecast horizon $H$. | |
| 39 | +\Cref{tab:lag_selection} reports the information criteria for VAR($p$) models of log realized volatility on the full trading-day panel. The Schwarz criterion selects $p = 3$, the Hannan--Quinn criterion $p = 4$ and the Akaike criterion $p = 5$; the baseline uses $p = 4$. | |
| 33 | 40 | |
| 34 | 41 | \begin{table}[htbp] |
| 35 | 42 | \centering |
| 36 | −\caption{Robustness to Forecast Horizon.} | |
| 37 | −\label{tab:robustness_horizon} | |
| 43 | +\caption{Information criteria for the lag order of the VAR, log realized volatility, 2016--2026.} | |
| 44 | +\label{tab:lag_selection} | |
| 45 | +\adjustbox{max width=\textwidth}{% | |
| 38 | 46 | \begin{threeparttable} |
| 39 | −\begin{tabular}{@{}lrrr@{}} | |
| 40 | −\toprule | |
| 41 | −& $H=5$ & $H=10$ (baseline) & $H=20$ \\ | |
| 42 | −\midrule | |
| 43 | −Total Spillover Index (\%) & 49.2 & 55.4 & 58.1 \\ | |
| 44 | −ES net spillover (\%) & $+$24.0 & $+$26.8 & $+$28.3 \\ | |
| 45 | −BTC own-shock (\%) & 82.6 & 79.3 & 77.1 \\ | |
| 46 | −\bottomrule | |
| 47 | −\end{tabular} | |
| 47 | +\input{tables/tab_lag_selection} | |
| 48 | 48 | \begin{tablenotes}[flushleft] |
| 49 | 49 | \footnotesize |
| 50 | −\item \textit{Notes:} Cross-asset spillovers increase with the horizon, as expected, but qualitative conclusions regarding the volatility hierarchy are robust. | |
| 50 | +\item \textit{Notes:} Akaike (AIC), Schwarz (BIC) and Hannan--Quinn (HQ) criteria for VAR($p$) with a constant, $p = 1, \ldots, 10$, computed on a common estimation sample; the minimum of each criterion is in bold. Source: \path{results/rev_table_lag_selection.csv}. | |
| 51 | 51 | \end{tablenotes} |
| 52 | −\end{threeparttable} | |
| 52 | +\end{threeparttable}} | |
| 53 | 53 | \end{table} |
| 54 | 54 | |
| 55 | −\newpage | |
| 56 | −\section{Summary of Key Numerical Results} | |
| 57 | −\label{sec:appendix_summary} | |
| 55 | +\section{Full Connectedness Tables by Regime} | |
| 56 | +\label{sec:appendix_regimes} | |
| 57 | + | |
| 58 | +\Cref{tab:regime_precovid,tab:regime_covid,tab:regime_ratehikes,tab:regime_etf} report the complete variance-decomposition tables for the four regimes summarized in \Cref{tab:regimes}. The COVID window uses $p = 1$; the others use $p = 4$. | |
| 58 | 59 | |
| 59 | 60 | \begin{table}[htbp] |
| 60 | 61 | \centering |
| 61 | −\caption{Summary of Key Findings.} | |
| 62 | −\label{tab:summary_findings} | |
| 63 | −\begin{tabular}{@{}p{7.5cm}r@{}} | |
| 64 | −\toprule | |
| 65 | −Metric & Value \\ | |
| 66 | −\midrule | |
| 67 | −Total Spillover Index (full sample) & 55.44\% \\ | |
| 68 | −Mean rolling TSI (200-day) & 67.13\% \\ | |
| 69 | −Maximum rolling TSI & 81.55\% \\ | |
| 70 | −Minimum rolling TSI & 57.22\% \\ | |
| 71 | −\midrule | |
| 72 | −Largest net transmitter (full sample) & ES: $+$26.80\% \\ | |
| 73 | −Second largest net transmitter & NQ: $+$19.72\% \\ | |
| 74 | −Largest net receiver (full sample) & VIX: $-$23.37\% \\ | |
| 75 | −\midrule | |
| 76 | −BTC own-shock contribution (full sample) & 79.33\% \\ | |
| 77 | −ETH own-shock contribution (full sample) & 77.88\% \\ | |
| 78 | −BTC--ETH pairwise spillover & 19.3\% / 20.6\% \\ | |
| 79 | −\midrule | |
| 80 | −TSI pre-COVID regime & 64.72\% \\ | |
| 81 | −TSI COVID crash regime & 66.66\% \\ | |
| 82 | −TSI rate-hiking regime & 65.62\% \\ | |
| 83 | −\midrule | |
| 84 | −BTC net spillover (pre-COVID) & $-$0.02\% \\ | |
| 85 | −BTC net spillover (COVID crash) & $-$21.34\% \\ | |
| 86 | −BTC net spillover (rate hikes) & $+$7.90\% \\ | |
| 87 | −\midrule | |
| 88 | −ES $\to$ VIX Granger $F$-statistic & 19.864 \\ | |
| 89 | −NQ $\to$ VIX Granger $F$-statistic & 16.708 \\ | |
| 90 | −\midrule | |
| 91 | −Mean annualized RV: ES & 13.85\% \\ | |
| 92 | −Mean annualized RV: BTC & 98.69\% \\ | |
| 93 | −Mean annualized RV: CL & 29.67\% \\ | |
| 94 | −Total 5-minute observations & $>$235 million \\ | |
| 95 | −\bottomrule | |
| 96 | −\end{tabular} | |
| 62 | +\caption{Connectedness table, pre-COVID regime (2019-01-01 to 2020-02-28), $T = 292$, VAR(4).} | |
| 63 | +\label{tab:regime_precovid} | |
| 64 | +\adjustbox{max width=\textwidth}{% | |
| 65 | +\input{tables/tab_regime_precovid} | |
| 66 | +} | |
| 97 | 67 | \end{table} |
| 68 | + | |
| 69 | +\begin{table}[htbp] | |
| 70 | +\centering | |
| 71 | +\caption{Connectedness table, COVID crash regime (2020-03-01 to 2020-06-30), $T = 85$, VAR(1).} | |
| 72 | +\label{tab:regime_covid} | |
| 73 | +\adjustbox{max width=\textwidth}{% | |
| 74 | +\input{tables/tab_regime_covid_crash} | |
| 75 | +} | |
| 76 | +\end{table} | |
| 77 | + | |
| 78 | +\begin{table}[htbp] | |
| 79 | +\centering | |
| 80 | +\caption{Connectedness table, rate-hiking regime (2022-01-01 to 2022-12-31), $T = 254$, VAR(4).} | |
| 81 | +\label{tab:regime_ratehikes} | |
| 82 | +\adjustbox{max width=\textwidth}{% | |
| 83 | +\input{tables/tab_regime_rate_hikes} | |
| 84 | +} | |
| 85 | +\end{table} | |
| 86 | + | |
| 87 | +\begin{table}[htbp] | |
| 88 | +\centering | |
| 89 | +\caption{Connectedness table, spot-ETF era (2024-01-11 to 2026-03-11), $T = 544$, VAR(4).} | |
| 90 | +\label{tab:regime_etf} | |
| 91 | +\adjustbox{max width=\textwidth}{% | |
| 92 | +\input{tables/tab_regime_spotetf_era} | |
| 93 | +} | |
| 94 | +\end{table} | |
| 95 | + | |
| 96 | +\section{Replication} | |
| 97 | +\label{sec:appendix_replication} | |
| 98 | + | |
| 99 | +The daily realized volatilities are produced by \path{scripts/01_analysis.py} from the vendor's 5-minute bars (about ten minutes and 8~GB of memory); all connectedness estimates, bootstrap intervals, robustness checks, rolling windows, regime and calendar-year tables and \Cref{fig:connectedness_heatmap,fig:rolling_spillover,fig:net_spillovers_regimes,fig:net_directional_btc_es,fig:network_graph,fig:yearly_integration} are produced by \path{scripts/02_connectedness_revision.py} from \path{results/daily_rv_all.csv} in about one minute; the intraday analysis of \Cref{sec:sessions} is produced by \path{scripts/03_intraday_sessions.py} from one-minute bars of the same vendor in about half a minute. Every table in the paper is generated by these scripts as a LaTeX fragment in \path{paper/tables/}. | |
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@@ -1,8 +1,9 @@ | ||
| 1 | 1 | % ============================================================================ |
| 2 | 2 | % UQO Working Paper No. 6 |
| 3 | 3 | % Intraday Volatility Transmission Across Asset Classes: |
| 4 | −% A Connectedness Analysis of Equities, Fixed Income, Commodities, | |
| 4 | +% A Connectedness Analysis of Equities, Foreign Exchange, Commodities, | |
| 5 | 5 | % and Cryptocurrencies |
| 6 | +% Version 1.1 -- revised after the editorial-board review of 2026-10-17 | |
| 6 | 7 | % ============================================================================ |
| 7 | 8 | \documentclass[12pt,letterpaper]{article} |
| 8 | 9 | |
@@ -67,9 +68,9 @@ | ||
| 67 | 68 | citecolor = NavyBlue, |
| 68 | 69 | urlcolor = NavyBlue, |
| 69 | 70 | pdfauthor = {Simon-Pierre Boucher}, |
| 70 | − pdftitle = {Intraday Volatility Transmission Across Asset Classes}, | |
| 71 | − pdfsubject = {Working Paper WP6}, | |
| 72 | − pdfkeywords = {realized volatility, spillovers, connectedness, high-frequency} | |
| 71 | + pdftitle = {Intraday Volatility Transmission Across Asset Classes: A Connectedness Analysis of Equities, Foreign Exchange, Commodities, and Cryptocurrencies}, | |
| 72 | + pdfsubject = {UQO Working Paper No. 6}, | |
| 73 | + pdfkeywords = {realized volatility, volatility spillovers, connectedness, high-frequency data, cryptocurrency} | |
| 73 | 74 | } |
| 74 | 75 | \usepackage{cleveref} |
| 75 | 76 | |
@@ -80,7 +81,7 @@ | ||
| 80 | 81 | % --- Bibliography --- |
| 81 | 82 | \usepackage{natbib} |
| 82 | 83 | \setcitestyle{authoryear,round,semicolon} |
| 83 | −\bibliographystyle{apalike} | |
| 84 | +\bibliographystyle{aer} | |
| 84 | 85 | |
| 85 | 86 | % --- Headers & Footers --- |
| 86 | 87 | \usepackage{fancyhdr} |
@@ -141,15 +142,15 @@ | ||
| 141 | 142 | % METADATA |
| 142 | 143 | % ============================================================================ |
| 143 | 144 | \newcommand{\WPnumber}{6} |
| 144 | −\newcommand{\WPtitle}{Intraday Volatility Transmission Across Asset Classes: A Connectedness Analysis of Equities, Fixed Income, Commodities, and Cryptocurrencies} | |
| 145 | +\newcommand{\WPtitle}{Intraday Volatility Transmission Across Asset Classes: A Connectedness Analysis of Equities, Foreign Exchange, Commodities, and Cryptocurrencies} | |
| 145 | 146 | \newcommand{\WPsubtitle}{} |
| 146 | −\newcommand{\WPdate}{May 2026} | |
| 147 | −\newcommand{\WPversion}{1.0} | |
| 147 | +\newcommand{\WPdate}{October 2026} | |
| 148 | +\newcommand{\WPversion}{1.1} | |
| 148 | 149 | \newcommand{\WPabstract}{% |
| 149 | −This paper investigates intraday volatility transmission across equities, foreign exchange, commodities, and cryptocurrency markets using 5-minute OHLCV data spanning 2008--2026. We construct daily realized volatility measures from over 235 million intraday observations across 10 representative instruments and apply the \citet{DieboldYilmaz2012} generalized variance decomposition framework within a VAR(4) model at a 10-day forecast horizon. Our full-sample analysis reveals a total spillover index of 55.44\%, with U.S.\ equity index futures (ES, NQ) serving as the dominant volatility transmitters (net spillovers of $+26.80\%$ and $+19.72\%$, respectively), while the VIX acts primarily as a volatility receiver ($-23.37\%$). Cryptocurrencies (BTC, ETH) remain largely isolated from traditional asset volatility networks, with own-shock contributions exceeding 77\%. Rolling 200-day connectedness analysis uncovers substantial time variation, with the total spillover index peaking at 81.55\% during the February 2018 volatility implosion. Regime-specific analysis reveals dramatic shifts in the volatility hierarchy: during the COVID-19 crash, USD/JPY emerges as the dominant shock originator ($+60.29\%$), while equity futures flip from transmitters to receivers. During the 2022 rate-hiking cycle, Bitcoin transitions to a net volatility transmitter ($+7.90\%$), suggesting growing integration of crypto markets with the traditional financial system. Intraday analysis of trading sessions shows that Bitcoin maintains near-uniform volatility across Asian, European, and U.S.\ hours, contrasting sharply with the session-dependent patterns of equity and VIX markets. Granger causality tests confirm that equity futures significantly lead VIX changes ($F=19.86$, $p<0.001$), while crypto markets remain causally independent. These findings have important implications for portfolio construction, risk management, and the monitoring of systemic risk across increasingly interconnected global markets.% | |
| 150 | +This paper measures how realized volatility is transmitted across equity index futures, major exchange rates, gold and crude oil futures, the VIX, and the two largest cryptocurrencies. Daily realized volatilities are built from 5-minute bars for ten instruments over 2008--2026, and the connectedness of their logarithms is estimated on the 2{,}514 trading days common to all series (March 2016--March 2026) with the generalized variance decomposition of a VAR(4) at a ten-day horizon \citep{DieboldYilmaz2012}, with residual-bootstrap confidence intervals. Cross-asset shocks account for 54.8\% (90\% interval 53.1--56.9) of forecast-error variance. E-mini S\&P~500 and Nasdaq~100 futures are the only robust net transmitters ($+36.0$ and $+25.6$ percentage points), while the realized volatility of the VIX ($-20.6$), crude oil ($-14.2$) and sterling ($-13.2$) are net receivers; the net positions of bitcoin and ether are statistically indistinguishable from zero. Bitcoin and ether form a tightly linked pair (27--28\% of each other's variance) whose exposure to traditional assets rises from under 10\% of forecast-error variance before 2020 to 20--46\% in 2020--2025, with information flowing predominantly from U.S. equities to crypto: in the 2024--2026 spot-ETF period bitcoin is a significant net receiver ($-12.4$, interval $-20.4$ to $-2.1$). Rolling estimates show that total connectedness rose during the COVID-19 crash and reached its highest level in 2025. Intraday, after converting exchange time stamps to UTC, equity and VIX volatility concentrate in the U.S. cash session (53--63\% of daily variance), whereas bitcoin's hourly profile is nearly flat (peak-to-trough ratio 1.2); U.S.-session equity volatility predicts bitcoin's next Asian-session volatility, but neither bitcoin's overnight nor its weekend volatility predicts U.S. equity volatility. The paper documents how calendar alignment of 24/7 and exchange-traded series materially affects connectedness estimates.% | |
| 150 | 151 | } |
| 151 | −\newcommand{\WPkeywords}{realized volatility, volatility spillovers, Diebold--Yilmaz connectedness, high-frequency data, cross-asset transmission, cryptocurrency, systemic risk} | |
| 152 | −\newcommand{\WPjel}{C32, C58, G12, G15, G17} | |
| 152 | +\newcommand{\WPkeywords}{realized volatility, volatility spillovers, connectedness, generalized variance decomposition, high-frequency data, cryptocurrency, trading sessions} | |
| 153 | +\newcommand{\WPjel}{C32, C58, G12, G15} | |
| 153 | 154 | |
| 154 | 155 | % --- Author --- |
| 155 | 156 | \newcommand{\WPauthor}{Simon-Pierre Boucher} |
@@ -187,7 +188,10 @@ This paper investigates intraday volatility transmission across equities, foreig | ||
| 187 | 188 | \input{sections/conclusion} |
| 188 | 189 | |
| 189 | 190 | % --- References --- |
| 190 | −\input{sections/references} | |
| 191 | +\newpage | |
| 192 | +\phantomsection | |
| 193 | +\addcontentsline{toc}{section}{References} | |
| 194 | +\bibliography{references} | |
| 191 | 195 | |
| 192 | 196 | % --- Appendix --- |
| 193 | 197 | \newpage |
added
paper/references.bib
+757 −0
@@ -0,0 +1,757 @@ | ||
| 1 | +% ============================================================================ | |
| 2 | +% UQO Working Paper No. 6 -- references.bib | |
| 3 | +% Every entry verified against Crossref on 2026-10-17 (editorial-board revision); | |
| 4 | +% DOIs recorded. See docs/CHANGELOG-REVISION.md for the verification log. | |
| 5 | +% ============================================================================ | |
| 6 | + | |
| 7 | +% ---------------------------------------------------------------- realized volatility | |
| 8 | +@article{Andersen1997, | |
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| 17 | +} | |
| 18 | + | |
| 19 | +@article{Andersen1998, | |
| 20 | + author = {Andersen, Torben G. and Bollerslev, Tim}, | |
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| 28 | +} | |
| 29 | + | |
| 30 | +@article{Andersen2001, | |
| 31 | + author = {Andersen, Torben G. and Bollerslev, Tim and Diebold, Francis X. and Labys, Paul}, | |
| 32 | + title = {The Distribution of Realized Exchange Rate Volatility}, | |
| 33 | + journal = {Journal of the American Statistical Association}, | |
| 34 | + year = {2001}, | |
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| 39 | +} | |
| 40 | + | |
| 41 | +@article{Andersen2003, | |
| 42 | + author = {Andersen, Torben G. and Bollerslev, Tim and Diebold, Francis X. and Labys, Paul}, | |
| 43 | + title = {Modeling and Forecasting Realized Volatility}, | |
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| 50 | +} | |
| 51 | + | |
| 52 | +@article{Andersen2007, | |
| 53 | + author = {Andersen, Torben G. and Bollerslev, Tim and Diebold, Francis X.}, | |
| 54 | + title = {Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility}, | |
| 55 | + journal = {Review of Economics and Statistics}, | |
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| 61 | +} | |
| 62 | + | |
| 63 | +@article{AitSahalia2005, | |
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| 70 | + pages = {351--416}, | |
| 71 | + doi = {10.1093/rfs/hhi016} | |
| 72 | +} | |
| 73 | + | |
| 74 | +@article{BarndorffNielsen2002, | |
| 75 | + author = {Barndorff-Nielsen, Ole E. and Shephard, Neil}, | |
| 76 | + title = {Econometric Analysis of Realized Volatility and Its Use in Estimating Stochastic Volatility Models}, | |
| 77 | + journal = {Journal of the Royal Statistical Society: Series B}, | |
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| 80 | + number = {2}, | |
| 81 | + pages = {253--280}, | |
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| 83 | +} | |
| 84 | + | |
| 85 | +@article{Bollerslev2016, | |
| 86 | + author = {Bollerslev, Tim and Patton, Andrew J. and Quaedvlieg, Rogier}, | |
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| 93 | + doi = {10.1016/j.jeconom.2015.10.007} | |
| 94 | +} | |
| 95 | + | |
| 96 | +@article{Corsi2009, | |
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| 99 | + journal = {Journal of Financial Econometrics}, | |
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| 105 | +} | |
| 106 | + | |
| 107 | +@article{HansenLunde2006, | |
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| 116 | +} | |
| 117 | + | |
| 118 | +@article{Liu2015, | |
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| 127 | +} | |
| 128 | + | |
| 129 | +@article{Zhang2005, | |
| 130 | + author = {Zhang, Lan and Mykland, Per A. and A{\"i}t-Sahalia, Yacine}, | |
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| 136 | + pages = {1394--1411}, | |
| 137 | + doi = {10.1198/016214505000000169} | |
| 138 | +} | |
| 139 | + | |
| 140 | +% ---------------------------------------------------------------- connectedness | |
| 141 | +@article{Antonakakis2020, | |
| 142 | + author = {Antonakakis, Nikolaos and Chatziantoniou, Ioannis and Gabauer, David}, | |
| 143 | + title = {Refined Measures of Dynamic Connectedness Based on Time-Varying Parameter Vector Autoregressions}, | |
| 144 | + journal = {Journal of Risk and Financial Management}, | |
| 145 | + year = {2020}, | |
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| 147 | + number = {4}, | |
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| 150 | +} | |
| 151 | + | |
| 152 | +@article{Barunik2016, | |
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| 155 | + journal = {Journal of Financial Markets}, | |
| 156 | + year = {2016}, | |
| 157 | + volume = {27}, | |
| 158 | + pages = {55--78}, | |
| 159 | + doi = {10.1016/j.finmar.2015.09.003} | |
| 160 | +} | |
| 161 | + | |
| 162 | +@article{Barunik2017, | |
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| 165 | + journal = {Journal of International Money and Finance}, | |
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| 168 | + pages = {39--56}, | |
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| 170 | +} | |
| 171 | + | |
| 172 | +@article{Barunik2018, | |
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| 175 | + journal = {Journal of Financial Econometrics}, | |
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| 181 | +} | |
| 182 | + | |
| 183 | +@article{Demirer2018, | |
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| 192 | +} | |
| 193 | + | |
| 194 | +@article{DieboldYilmaz2009, | |
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| 203 | +} | |
| 204 | + | |
| 205 | +@article{DieboldYilmaz2012, | |
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| 214 | +} | |
| 215 | + | |
| 216 | +@article{DieboldYilmaz2014, | |
| 217 | + author = {Diebold, Francis X. and Yilmaz, Kamil}, | |
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| 225 | +} | |
| 226 | + | |
| 227 | +@article{DieboldYilmaz2016, | |
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| 279 | + | |
| 280 | +% ---------------------------------------------------------------- time-series econometrics | |
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| 332 | +} | |
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| 340 | + doi = {10.1007/978-3-540-27752-1} | |
| 341 | +} | |
| 342 | + | |
| 343 | +@article{NeweyWest1987, | |
| 344 | + author = {Newey, Whitney K. and West, Kenneth D.}, | |
| 345 | + title = {A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix}, | |
| 346 | + journal = {Econometrica}, | |
| 347 | + year = {1987}, | |
| 348 | + volume = {55}, | |
| 349 | + number = {3}, | |
| 350 | + pages = {703--708}, | |
| 351 | + doi = {10.2307/1913610} | |
| 352 | +} | |
| 353 | + | |
| 354 | +% ---------------------------------------------------------------- volatility transmission, contagion, multivariate GARCH | |
| 355 | +@article{Ang2002, | |
| 356 | + author = {Ang, Andrew and Bekaert, Geert}, | |
| 357 | + title = {International Asset Allocation with Regime Shifts}, | |
| 358 | + journal = {Review of Financial Studies}, | |
| 359 | + year = {2002}, | |
| 360 | + volume = {15}, | |
| 361 | + number = {4}, | |
| 362 | + pages = {1137--1187}, | |
| 363 | + doi = {10.1093/rfs/15.4.1137} | |
| 364 | +} | |
| 365 | + | |
| 366 | +@article{Baele2005, | |
| 367 | + author = {Baele, Lieven}, | |
| 368 | + title = {Volatility Spillover Effects in {European} Equity Markets}, | |
| 369 | + journal = {Journal of Financial and Quantitative Analysis}, | |
| 370 | + year = {2005}, | |
| 371 | + volume = {40}, | |
| 372 | + number = {2}, | |
| 373 | + pages = {373--401}, | |
| 374 | + doi = {10.1017/S0022109000002350} | |
| 375 | +} | |
| 376 | + | |
| 377 | +@article{Engle2002, | |
| 378 | + author = {Engle, Robert}, | |
| 379 | + title = {Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models}, | |
| 380 | + journal = {Journal of Business \& Economic Statistics}, | |
| 381 | + year = {2002}, | |
| 382 | + volume = {20}, | |
| 383 | + number = {3}, | |
| 384 | + pages = {339--350}, | |
| 385 | + doi = {10.1198/073500102288618487} | |
| 386 | +} | |
| 387 | + | |
| 388 | +@article{Fama1965, | |
| 389 | + author = {Fama, Eugene F.}, | |
| 390 | + title = {The Behavior of Stock-Market Prices}, | |
| 391 | + journal = {Journal of Business}, | |
| 392 | + year = {1965}, | |
| 393 | + volume = {38}, | |
| 394 | + number = {1}, | |
| 395 | + pages = {34--105}, | |
| 396 | + doi = {10.1086/294743} | |
| 397 | +} | |
| 398 | + | |
| 399 | +@article{Forbes2002, | |
| 400 | + author = {Forbes, Kristin J. and Rigobon, Roberto}, | |
| 401 | + title = {No Contagion, Only Interdependence: Measuring Stock Market Comovements}, | |
| 402 | + journal = {Journal of Finance}, | |
| 403 | + year = {2002}, | |
| 404 | + volume = {57}, | |
| 405 | + number = {5}, | |
| 406 | + pages = {2223--2261}, | |
| 407 | + doi = {10.1111/0022-1082.00494} | |
| 408 | +} | |
| 409 | + | |
| 410 | +@article{Hamao1990, | |
| 411 | + author = {Hamao, Yasushi and Masulis, Ronald W. and Ng, Victor}, | |
| 412 | + title = {Correlations in Price Changes and Volatility across International Stock Markets}, | |
| 413 | + journal = {Review of Financial Studies}, | |
| 414 | + year = {1990}, | |
| 415 | + volume = {3}, | |
| 416 | + number = {2}, | |
| 417 | + pages = {281--307}, | |
| 418 | + doi = {10.1093/rfs/3.2.281} | |
| 419 | +} | |
| 420 | + | |
| 421 | +@article{King1990, | |
| 422 | + author = {King, Mervyn A. and Wadhwani, Sushil}, | |
| 423 | + title = {Transmission of Volatility between Stock Markets}, | |
| 424 | + journal = {Review of Financial Studies}, | |
| 425 | + year = {1990}, | |
| 426 | + volume = {3}, | |
| 427 | + number = {1}, | |
| 428 | + pages = {5--33}, | |
| 429 | + doi = {10.1093/rfs/3.1.5} | |
| 430 | +} | |
| 431 | + | |
| 432 | +@article{Lin1994, | |
| 433 | + author = {Lin, Wen-Ling and Engle, Robert F. and Ito, Takatoshi}, | |
| 434 | + title = {Do Bulls and Bears Move across Borders? {International} Transmission of Stock Returns and Volatility}, | |
| 435 | + journal = {Review of Financial Studies}, | |
| 436 | + year = {1994}, | |
| 437 | + volume = {7}, | |
| 438 | + number = {3}, | |
| 439 | + pages = {507--538}, | |
| 440 | + doi = {10.1093/rfs/7.3.507} | |
| 441 | +} | |
| 442 | + | |
| 443 | +@article{Longin2001, | |
| 444 | + author = {Longin, Fran{\c{c}}ois and Solnik, Bruno}, | |
| 445 | + title = {Extreme Correlation of International Equity Markets}, | |
| 446 | + journal = {Journal of Finance}, | |
| 447 | + year = {2001}, | |
| 448 | + volume = {56}, | |
| 449 | + number = {2}, | |
| 450 | + pages = {649--676}, | |
| 451 | + doi = {10.1111/0022-1082.00340} | |
| 452 | +} | |
| 453 | + | |
| 454 | +@article{Mandelbrot1963, | |
| 455 | + author = {Mandelbrot, Benoit}, | |
| 456 | + title = {The Variation of Certain Speculative Prices}, | |
| 457 | + journal = {Journal of Business}, | |
| 458 | + year = {1963}, | |
| 459 | + volume = {36}, | |
| 460 | + number = {4}, | |
| 461 | + pages = {394--419}, | |
| 462 | + doi = {10.1086/294632} | |
| 463 | +} | |
| 464 | + | |
| 465 | +% ---------------------------------------------------------------- FX, commodities, VIX | |
| 466 | +@article{Arouri2011, | |
| 467 | + author = {Arouri, Mohamed El Hedi and Jouini, Jamel and Nguyen, Duc Khuong}, | |
| 468 | + title = {Volatility Spillovers between Oil Prices and Stock Sector Returns: Implications for Portfolio Management}, | |
| 469 | + journal = {Journal of International Money and Finance}, | |
| 470 | + year = {2011}, | |
| 471 | + volume = {30}, | |
| 472 | + number = {7}, | |
| 473 | + pages = {1387--1405}, | |
| 474 | + doi = {10.1016/j.jimonfin.2011.07.008} | |
| 475 | +} | |
| 476 | + | |
| 477 | +@article{Baur2010, | |
| 478 | + author = {Baur, Dirk G. and Lucey, Brian M.}, | |
| 479 | + title = {Is Gold a Hedge or a Safe Haven? {An} Analysis of Stocks, Bonds and Gold}, | |
| 480 | + journal = {Financial Review}, | |
| 481 | + year = {2010}, | |
| 482 | + volume = {45}, | |
| 483 | + number = {2}, | |
| 484 | + pages = {217--229}, | |
| 485 | + doi = {10.1111/j.1540-6288.2010.00244.x} | |
| 486 | +} | |
| 487 | + | |
| 488 | +@article{BekaertHoerova2014, | |
| 489 | + author = {Bekaert, Geert and Hoerova, Marie}, | |
| 490 | + title = {The {VIX}, the Variance Premium and Stock Market Volatility}, | |
| 491 | + journal = {Journal of Econometrics}, | |
| 492 | + year = {2014}, | |
| 493 | + volume = {183}, | |
| 494 | + number = {2}, | |
| 495 | + pages = {181--192}, | |
| 496 | + doi = {10.1016/j.jeconom.2014.05.008} | |
| 497 | +} | |
| 498 | + | |
| 499 | +@article{Habib2012, | |
| 500 | + author = {Habib, Maurizio M. and Stracca, Livio}, | |
| 501 | + title = {Getting beyond Carry Trade: What Makes a Safe Haven Currency?}, | |
| 502 | + journal = {Journal of International Economics}, | |
| 503 | + year = {2012}, | |
| 504 | + volume = {87}, | |
| 505 | + number = {1}, | |
| 506 | + pages = {50--64}, | |
| 507 | + doi = {10.1016/j.jinteco.2011.12.005} | |
| 508 | +} | |
| 509 | + | |
| 510 | +@article{Kang2017, | |
| 511 | + author = {Kang, Sang Hoon and McIver, Ron and Yoon, Seong-Min}, | |
| 512 | + title = {Dynamic Spillover Effects among Crude Oil, Precious Metal, and Agricultural Commodity Futures Markets}, | |
| 513 | + journal = {Energy Economics}, | |
| 514 | + year = {2017}, | |
| 515 | + volume = {62}, | |
| 516 | + pages = {19--32}, | |
| 517 | + doi = {10.1016/j.eneco.2016.12.011} | |
| 518 | +} | |
| 519 | + | |
| 520 | +@article{Mensi2013, | |
| 521 | + author = {Mensi, Walid and Beljid, Makram and Boubaker, Adel and Managi, Shunsuke}, | |
| 522 | + title = {Correlations and Volatility Spillovers across Commodity and Stock Markets: Linking Energies, Food, and Gold}, | |
| 523 | + journal = {Economic Modelling}, | |
| 524 | + year = {2013}, | |
| 525 | + volume = {32}, | |
| 526 | + pages = {15--22}, | |
| 527 | + doi = {10.1016/j.econmod.2013.01.023} | |
| 528 | +} | |
| 529 | + | |
| 530 | +@article{Ranaldo2010, | |
| 531 | + author = {Ranaldo, Angelo and S{\"o}derlind, Paul}, | |
| 532 | + title = {Safe Haven Currencies}, | |
| 533 | + journal = {Review of Finance}, | |
| 534 | + year = {2010}, | |
| 535 | + volume = {14}, | |
| 536 | + number = {3}, | |
| 537 | + pages = {385--407}, | |
| 538 | + doi = {10.1093/rof/rfq007} | |
| 539 | +} | |
| 540 | + | |
| 541 | +@article{Reboredo2013, | |
| 542 | + author = {Reboredo, Juan C.}, | |
| 543 | + title = {Is Gold a Safe Haven or a Hedge for the {US} Dollar? {Implications} for Risk Management}, | |
| 544 | + journal = {Journal of Banking \& Finance}, | |
| 545 | + year = {2013}, | |
| 546 | + volume = {37}, | |
| 547 | + number = {8}, | |
| 548 | + pages = {2665--2676}, | |
| 549 | + doi = {10.1016/j.jbankfin.2013.03.020} | |
| 550 | +} | |
| 551 | + | |
| 552 | +@article{Vivian2012, | |
| 553 | + author = {Vivian, Andrew and Wohar, Mark E.}, | |
| 554 | + title = {Commodity Volatility Breaks}, | |
| 555 | + journal = {Journal of International Financial Markets, Institutions and Money}, | |
| 556 | + year = {2012}, | |
| 557 | + volume = {22}, | |
| 558 | + number = {2}, | |
| 559 | + pages = {395--422}, | |
| 560 | + doi = {10.1016/j.intfin.2011.12.003} | |
| 561 | +} | |
| 562 | + | |
| 563 | +@article{Whaley2009, | |
| 564 | + author = {Whaley, Robert E.}, | |
| 565 | + title = {Understanding the {VIX}}, | |
| 566 | + journal = {Journal of Portfolio Management}, | |
| 567 | + year = {2009}, | |
| 568 | + volume = {35}, | |
| 569 | + number = {3}, | |
| 570 | + pages = {98--105}, | |
| 571 | + doi = {10.3905/jpm.2009.35.3.098} | |
| 572 | +} | |
| 573 | + | |
| 574 | +% ---------------------------------------------------------------- cryptocurrencies | |
| 575 | +@article{Baur2018, | |
| 576 | + author = {Baur, Dirk G. and Hong, KiHoon and Lee, Adrian D.}, | |
| 577 | + title = {Bitcoin: Medium of Exchange or Speculative Assets?}, | |
| 578 | + journal = {Journal of International Financial Markets, Institutions and Money}, | |
| 579 | + year = {2018}, | |
| 580 | + volume = {54}, | |
| 581 | + pages = {177--189}, | |
| 582 | + doi = {10.1016/j.intfin.2017.12.004} | |
| 583 | +} | |
| 584 | + | |
| 585 | +@article{Baur2019, | |
| 586 | + author = {Baur, Dirk G. and Cahill, Daniel and Godfrey, Keith and Liu, Zhangxin (Frank)}, | |
| 587 | + title = {Bitcoin Time-of-Day, Day-of-Week and Month-of-Year Effects in Returns and Trading Volume}, | |
| 588 | + journal = {Finance Research Letters}, | |
| 589 | + year = {2019}, | |
| 590 | + volume = {31}, | |
| 591 | + pages = {78--92}, | |
| 592 | + doi = {10.1016/j.frl.2019.04.023} | |
| 593 | +} | |
| 594 | + | |
| 595 | +@article{Bouri2017, | |
| 596 | + author = {Bouri, Elie and Moln{\'a}r, Peter and Azzi, Georges and Roubaud, David and Hagfors, Lars Ivar}, | |
| 597 | + title = {On the Hedge and Safe Haven Properties of {Bitcoin}: Is It Really More than a Diversifier?}, | |
| 598 | + journal = {Finance Research Letters}, | |
| 599 | + year = {2017}, | |
| 600 | + volume = {20}, | |
| 601 | + pages = {192--198}, | |
| 602 | + doi = {10.1016/j.frl.2016.09.025} | |
| 603 | +} | |
| 604 | + | |
| 605 | +@article{Bouri2020, | |
| 606 | + author = {Bouri, Elie and Shahzad, Syed Jawad Hussain and Roubaud, David and Kristoufek, Ladislav and Lucey, Brian}, | |
| 607 | + title = {Bitcoin, Gold, and Commodities as Safe Havens for Stocks: New Insight through Wavelet Analysis}, | |
| 608 | + journal = {Quarterly Review of Economics and Finance}, | |
| 609 | + year = {2020}, | |
| 610 | + volume = {77}, | |
| 611 | + pages = {156--164}, | |
| 612 | + doi = {10.1016/j.qref.2020.03.004} | |
| 613 | +} | |
| 614 | + | |
| 615 | +@article{Chaim2018, | |
| 616 | + author = {Chaim, Pedro and Laurini, M{\'a}rcio P.}, | |
| 617 | + title = {Volatility and Return Jumps in Bitcoin}, | |
| 618 | + journal = {Economics Letters}, | |
| 619 | + year = {2018}, | |
| 620 | + volume = {173}, | |
| 621 | + pages = {158--163}, | |
| 622 | + doi = {10.1016/j.econlet.2018.10.011} | |
| 623 | +} | |
| 624 | + | |
| 625 | +@article{ConlonMcGee2020, | |
| 626 | + author = {Conlon, Thomas and McGee, Richard}, | |
| 627 | + title = {Safe Haven or Risky Hazard? {Bitcoin} during the {COVID-19} Bear Market}, | |
| 628 | + journal = {Finance Research Letters}, | |
| 629 | + year = {2020}, | |
| 630 | + volume = {35}, | |
| 631 | + pages = {101607}, | |
| 632 | + doi = {10.1016/j.frl.2020.101607} | |
| 633 | +} | |
| 634 | + | |
| 635 | +@article{Corbet2018, | |
| 636 | + author = {Corbet, Shaen and Meegan, Andrew and Larkin, Charles and Lucey, Brian and Yarovaya, Larisa}, | |
| 637 | + title = {Exploring the Dynamic Relationships between Cryptocurrencies and Other Financial Assets}, | |
| 638 | + journal = {Economics Letters}, | |
| 639 | + year = {2018}, | |
| 640 | + volume = {165}, | |
| 641 | + pages = {28--34}, | |
| 642 | + doi = {10.1016/j.econlet.2018.01.004} | |
| 643 | +} | |
| 644 | + | |
| 645 | +@article{Corbet2020, | |
| 646 | + author = {Corbet, Shaen and Larkin, Charles and Lucey, Brian}, | |
| 647 | + title = {The Contagion Effects of the {COVID-19} Pandemic: Evidence from Gold and Cryptocurrencies}, | |
| 648 | + journal = {Finance Research Letters}, | |
| 649 | + year = {2020}, | |
| 650 | + volume = {35}, | |
| 651 | + pages = {101554}, | |
| 652 | + doi = {10.1016/j.frl.2020.101554} | |
| 653 | +} | |
| 654 | + | |
| 655 | +@article{Elsayed2022, | |
| 656 | + author = {Elsayed, Ahmed H. and Gozgor, Giray and Lau, Chi Keung Marco}, | |
| 657 | + title = {Risk Transmissions between Bitcoin and Traditional Financial Assets during the {COVID-19} Era: The Role of Global Uncertainties}, | |
| 658 | + journal = {International Review of Financial Analysis}, | |
| 659 | + year = {2022}, | |
| 660 | + volume = {81}, | |
| 661 | + pages = {102069}, | |
| 662 | + doi = {10.1016/j.irfa.2022.102069} | |
| 663 | +} | |
| 664 | + | |
| 665 | +@article{Eross2019, | |
| 666 | + author = {Eross, Andrea and McGroarty, Frank and Urquhart, Andrew and Wolfe, Simon}, | |
| 667 | + title = {The Intraday Dynamics of Bitcoin}, | |
| 668 | + journal = {Research in International Business and Finance}, | |
| 669 | + year = {2019}, | |
| 670 | + volume = {49}, | |
| 671 | + pages = {71--81}, | |
| 672 | + doi = {10.1016/j.ribaf.2019.01.008} | |
| 673 | +} | |
| 674 | + | |
| 675 | +@techreport{Iyer2022, | |
| 676 | + author = {Iyer, Tara}, | |
| 677 | + title = {Cryptic Connections: Spillovers between Crypto and Equity Markets}, | |
| 678 | + institution = {International Monetary Fund}, | |
| 679 | + type = {Global Financial Stability Notes}, | |
| 680 | + number = {2022/001}, | |
| 681 | + year = {2022}, | |
| 682 | + doi = {10.5089/9781616358068.065} | |
| 683 | +} | |
| 684 | + | |
| 685 | +@article{Ji2019a, | |
| 686 | + author = {Ji, Qiang and Bouri, Elie and Lau, Chi Keung Marco and Roubaud, David}, | |
| 687 | + title = {Dynamic Connectedness and Integration in Cryptocurrency Markets}, | |
| 688 | + journal = {International Review of Financial Analysis}, | |
| 689 | + year = {2019}, | |
| 690 | + volume = {63}, | |
| 691 | + pages = {257--272}, | |
| 692 | + doi = {10.1016/j.irfa.2018.12.002} | |
| 693 | +} | |
| 694 | + | |
| 695 | +@article{Ji2019b, | |
| 696 | + author = {Ji, Qiang and Bouri, Elie and Roubaud, David and Kristoufek, Ladislav}, | |
| 697 | + title = {Information Interdependence among Energy, Cryptocurrency and Major Commodity Markets}, | |
| 698 | + journal = {Energy Economics}, | |
| 699 | + year = {2019}, | |
| 700 | + volume = {81}, | |
| 701 | + pages = {1042--1055}, | |
| 702 | + doi = {10.1016/j.eneco.2019.06.005} | |
| 703 | +} | |
| 704 | + | |
| 705 | +@article{Katsiampa2017, | |
| 706 | + author = {Katsiampa, Paraskevi}, | |
| 707 | + title = {Volatility Estimation for {Bitcoin}: A Comparison of {GARCH} Models}, | |
| 708 | + journal = {Economics Letters}, | |
| 709 | + year = {2017}, | |
| 710 | + volume = {158}, | |
| 711 | + pages = {3--6}, | |
| 712 | + doi = {10.1016/j.econlet.2017.06.023} | |
| 713 | +} | |
| 714 | + | |
| 715 | +@article{Makarov2020, | |
| 716 | + author = {Makarov, Igor and Schoar, Antoinette}, | |
| 717 | + title = {Trading and Arbitrage in Cryptocurrency Markets}, | |
| 718 | + journal = {Journal of Financial Economics}, | |
| 719 | + year = {2020}, | |
| 720 | + volume = {135}, | |
| 721 | + number = {2}, | |
| 722 | + pages = {293--319}, | |
| 723 | + doi = {10.1016/j.jfineco.2019.07.001} | |
| 724 | +} | |
| 725 | + | |
| 726 | +@article{Yousaf2023, | |
| 727 | + author = {Yousaf, Imran and Pham, Linh and Goodell, John W.}, | |
| 728 | + title = {The Connectedness between Meme Tokens, Meme Stocks, and Other Asset Classes: Evidence from a Quantile Connectedness Approach}, | |
| 729 | + journal = {Journal of International Financial Markets, Institutions and Money}, | |
| 730 | + year = {2023}, | |
| 731 | + volume = {82}, | |
| 732 | + pages = {101694}, | |
| 733 | + doi = {10.1016/j.intfin.2022.101694} | |
| 734 | +} | |
| 735 | + | |
| 736 | +% ---------------------------------------------------------------- intraday patterns in equities | |
| 737 | +@article{Harris1986, | |
| 738 | + author = {Harris, Lawrence}, | |
| 739 | + title = {A Transaction Data Study of Weekly and Intradaily Patterns in Stock Returns}, | |
| 740 | + journal = {Journal of Financial Economics}, | |
| 741 | + year = {1986}, | |
| 742 | + volume = {16}, | |
| 743 | + number = {1}, | |
| 744 | + pages = {99--117}, | |
| 745 | + doi = {10.1016/0304-405X(86)90044-9} | |
| 746 | +} | |
| 747 | + | |
| 748 | +@article{Wood1985, | |
| 749 | + author = {Wood, Robert A. and McInish, Thomas H. and Ord, J. Keith}, | |
| 750 | + title = {An Investigation of Transactions Data for {NYSE} Stocks}, | |
| 751 | + journal = {Journal of Finance}, | |
| 752 | + year = {1985}, | |
| 753 | + volume = {40}, | |
| 754 | + number = {3}, | |
| 755 | + pages = {723--739}, | |
| 756 | + doi = {10.1111/j.1540-6261.1985.tb04996.x} | |
| 757 | +} | |
modified
paper/sections/conclusion.tex
+4 −6
@@ -3,12 +3,10 @@ | ||
| 3 | 3 | \label{sec:conclusion} |
| 4 | 4 | % ============================================================================ |
| 5 | 5 | |
| 6 | −This paper provides a comprehensive analysis of intraday volatility transmission across equities, foreign exchange, commodities, and cryptocurrency markets using 5-minute OHLCV data spanning 2008--2026. Employing the \citet{DieboldYilmaz2012} generalized variance decomposition framework within a VAR(4) model, we document several important findings. | |
| 6 | +This paper has measured the transmission of realized volatility across equity index futures, major exchange rates, gold and crude oil futures, the VIX and the two largest cryptocurrencies, using daily realized volatilities built from 5-minute bars and the generalized variance decomposition of a VAR estimated on the 2{,}514 trading days common to all ten series between March 2016 and March 2026. Cross-asset shocks account for 54.8\% of forecast-error variance. The E-mini S\&P~500 and Nasdaq~100 futures are the only robust net transmitters; the realized volatility of the VIX, crude oil and sterling are robust net receivers; and the net positions of the euro, the yen, gold, bitcoin and ether cannot be distinguished from zero over the decade. These conclusions hold across lag orders, forecast horizons, the treatment of weekend crypto variance, and the inclusion or exclusion of the VIX and of the cryptocurrencies. | |
| 7 | 7 | |
| 8 | −The full-sample analysis reveals a total spillover index of 55.44\%, with U.S.\ equity index futures serving as the dominant volatility transmitters and the VIX acting primarily as a volatility receiver. Cryptocurrencies remain largely isolated from the traditional asset volatility network, though this isolation is diminishing over time. | |
| 8 | +The cryptocurrencies form a tightly linked pair whose exposure to the traditional system has grown from under 10\% of forecast-error variance before 2020 to between 20\% and 46\% since, with the net flow running from U.S. equities to crypto: bitcoin and ether are significant net receivers in the spot-ETF period, the previous day's U.S.-session volatility of equity futures predicts bitcoin's Asian-session volatility, and neither bitcoin's overnight nor its weekend volatility predicts the U.S.-session volatility of equity futures. Total connectedness rose during the COVID-19 crash, when exchange-rate volatility became the common factor, and reached its highest level of the sample in 2025. Intraday, equity and VIX volatility are concentrated in the U.S. cash session while bitcoin's volatility is nearly uniform across the day and the week. | |
| 9 | 9 | |
| 10 | −Regime-specific analysis uncovers dramatic shifts: during the COVID-19 crash, USD/JPY emerges as the dominant shock originator, while during the 2022 rate-hiking cycle, Bitcoin transitions to a net volatility transmitter ($+7.9\%$). The rolling connectedness analysis demonstrates the TSI's potential as a systemic risk indicator, with the index rising before and during major market dislocations. | |
| 10 | +The revision of this paper has also been an exercise in the sensitivity of connectedness measures to data construction. Aligning 24/7 and exchange-traded series on a common trading calendar, rather than forward-filling the latter over weekends, changed the total index by five percentage points, the net spillover of equity futures by fifteen, and the apparent isolation of the crypto block from near-complete to partial; attaching bootstrap intervals to regime estimates showed that several sign changes reported in the earlier version, and in parts of the literature, are within sampling error; and converting exchange time stamps to UTC relocated the intraday volatility peaks from the European to the U.S. session. We regard these corrections as part of the paper's contribution. | |
| 11 | 11 | |
| 12 | −Bitcoin's 24/7 market structure generates a remarkably uniform volatility profile across global trading sessions, contrasting with the session-dependent patterns of equity and VIX markets. Granger causality tests confirm the primacy of equity futures in driving VIX movements and the causal independence of Bitcoin. | |
| 13 | − | |
| 14 | −Future research could extend this analysis by incorporating frequency-domain decompositions \citep{Barunik2018} to distinguish short-run from long-run spillovers, employing TVP-VAR models \citep{Antonakakis2020} to avoid rolling-window smoothing, and examining the role of crypto-specific events in shaping the crypto--traditional market volatility nexus. | |
| 12 | +Three extensions appear most promising. A frequency decomposition of connectedness \citep{Barunik2018} would show whether the equity-to-crypto transmission documented here operates at short or long horizons. A time-varying-parameter VAR \citep{Antonakakis2020} or a shrinkage estimator would recover time variation in the hierarchy with fewer effective parameters than rolling windows and would allow a formal test of the 2020 break in crypto integration. And jump-robust, single-exchange realized measures for the cryptocurrencies, together with the removal of futures roll returns, would tighten the measurement side on which the whole analysis rests. | |
modified
paper/sections/data.tex
+47 −32
@@ -3,50 +3,56 @@ | ||
| 3 | 3 | \label{sec:data} |
| 4 | 4 | % ============================================================================ |
| 5 | 5 | |
| 6 | −\subsection{Data Sources and Description} | |
| 6 | +\subsection{Sources and Instruments} | |
| 7 | 7 | |
| 8 | −We employ 5-minute OHLCV (Open, High, Low, Close, Volume) data from four DuckDB databases covering four major asset classes. The databases collectively contain over 235 million intraday observations spanning January 2008 to March 2026. \Cref{tab:asset_universe} details the 10 representative instruments selected for the analysis. | |
| 8 | +The raw data are 5-minute open--high--low--close--volume bars supplied by FirstRate Data and stored in four DuckDB databases: continuous front-month futures (ES, NQ, GC, CL), spot exchange rates (EUR/USD, USD/JPY, GBP/USD), spot cryptocurrency prices in U.S. dollars (BTC, ETH) and the CBOE Volatility Index. Together the ten series contain about 235 million bars between January 2008 and March 2026. \Cref{tab:asset_universe} lists the instruments. They were chosen to be the most liquid representative of each asset class, to overlap over a decade, and to differ in trading hours: the futures trade almost continuously from Sunday evening to Friday afternoon with a daily one-hour maintenance break, the exchange rates trade continuously from Sunday evening to Friday evening, the cryptocurrencies trade every hour of every day, and the VIX is disseminated by CBOE only between 03:15 and 16:15 Eastern time (09:30--16:15 before April 2016) on U.S. trading days. | |
| 9 | 9 | |
| 10 | 10 | \begin{table}[htbp] |
| 11 | 11 | \centering |
| 12 | −\caption{Asset Universe.} | |
| 12 | +\caption{Asset universe.} | |
| 13 | 13 | \label{tab:asset_universe} |
| 14 | +\adjustbox{max width=\textwidth}{% | |
| 14 | 15 | \begin{threeparttable} |
| 15 | −\begin{tabular}{@{}llll@{}} | |
| 16 | +\begin{tabular}{@{}lllll@{}} | |
| 16 | 17 | \toprule |
| 17 | −Asset Class & Symbol & Description & Source \\ | |
| 18 | +Asset class & Symbol & Instrument & Venue & Trading hours \\ | |
| 18 | 19 | \midrule |
| 19 | −\multirow{2}{*}{Equity} & ES & E-Mini S\&P 500 Futures & Futures \\ | |
| 20 | − & NQ & E-Mini Nasdaq 100 Futures & Futures \\[3pt] | |
| 21 | −\multirow{3}{*}{FX} & EURUSD & Euro / U.S.\ Dollar & FX \\ | |
| 22 | − & USDJPY & U.S.\ Dollar / Japanese Yen & FX \\ | |
| 23 | − & GBPUSD & British Pound / U.S.\ Dollar & FX \\[3pt] | |
| 24 | −\multirow{2}{*}{Commodity} & GC & Gold Futures (COMEX) & Futures \\ | |
| 25 | − & CL & WTI Crude Oil Futures & Futures \\[3pt] | |
| 26 | −\multirow{2}{*}{Crypto} & BTC & Bitcoin (spot) & Crypto \\ | |
| 27 | − & ETH & Ethereum (spot) & Crypto \\[3pt] | |
| 28 | −Volatility & VIX & CBOE Volatility Index & Index \\ | |
| 20 | +\multirow{2}{*}{Equity} & ES & E-mini S\&P 500 futures & CME Globex & Sun 18:00--Fri 17:00 ET, break 17:00--18:00 \\ | |
| 21 | + & NQ & E-mini Nasdaq 100 futures & CME Globex & Sun 18:00--Fri 17:00 ET, break 17:00--18:00 \\[3pt] | |
| 22 | +\multirow{3}{*}{FX} & EURUSD & Euro / U.S.\ dollar & Interbank spot & Sun 17:00--Fri 17:00 ET \\ | |
| 23 | + & USDJPY & U.S.\ dollar / Japanese yen & Interbank spot & Sun 17:00--Fri 17:00 ET \\ | |
| 24 | + & GBPUSD & British pound / U.S.\ dollar & Interbank spot & Sun 17:00--Fri 17:00 ET \\[3pt] | |
| 25 | +\multirow{2}{*}{Commodity} & GC & Gold futures & COMEX & Sun 18:00--Fri 17:00 ET, break 17:00--18:00 \\ | |
| 26 | + & CL & WTI crude oil futures & NYMEX & Sun 18:00--Fri 17:00 ET, break 17:00--18:00 \\[3pt] | |
| 27 | +\multirow{2}{*}{Crypto} & BTC & Bitcoin, spot, USD & Composite of exchanges & 24 hours, 7 days \\ | |
| 28 | + & ETH & Ether, spot, USD & Composite of exchanges & 24 hours, 7 days \\[3pt] | |
| 29 | +Volatility & VIX & CBOE Volatility Index & CBOE & 03:15--16:15 ET on U.S. trading days \\ | |
| 29 | 30 | \bottomrule |
| 30 | 31 | \end{tabular} |
| 31 | 32 | \begin{tablenotes}[flushleft] |
| 32 | 33 | \footnotesize |
| 33 | −\item \textit{Notes:} All data are 5-minute OHLCV bars stored in DuckDB databases. Source column indicates the database of origin. | |
| 34 | +\item \textit{Notes:} 5-minute bars from FirstRate Data; futures are continuous front-month series. ET denotes U.S. Eastern time. The VIX is an index, not a traded instrument; its ``realized volatility'' is the realized volatility of 5-minute changes in the index. | |
| 34 | 35 | \end{tablenotes} |
| 35 | −\end{threeparttable} | |
| 36 | +\end{threeparttable}} | |
| 36 | 37 | \end{table} |
| 37 | 38 | |
| 38 | −The selection of assets is guided by: (i)~liquidity and representativeness within each asset class; (ii)~sufficient overlap in sample periods; (iii)~diversity in trading hours; and (iv)~economic significance for volatility transmission analysis. | |
| 39 | +\subsection{Time Stamps and Alignment} | |
| 40 | +\label{sec:alignment} | |
| 39 | 41 | |
| 40 | −\subsection{Descriptive Statistics of Intraday Returns} | |
| 42 | +All FirstRate time stamps are expressed in U.S. Eastern time, which we verified from the location of the daily Globex maintenance break (17:00--18:00) in the futures series and of the opening bar of the VIX series (03:15 or 09:30). A calendar day is therefore an Eastern-time day, and the daily realized volatility of a futures contract on day $t$ aggregates the bars between 00:00 and 24:00 Eastern of that day, that is, the second part of the overnight Globex session that opened the previous evening, the cash session, and the first hours of the following Globex session. This definition is common to all exchange-traded series and to the cryptocurrencies, whose trading is uninterrupted. The earlier version of this paper treated the time stamps as UTC; the intraday results of \Cref{sec:sessions} are based on an explicit conversion from Eastern time to UTC. | |
| 41 | 43 | |
| 42 | −\Cref{tab:descriptive_stats} presents descriptive statistics for 5-minute log returns across all 10 assets. | |
| 44 | +A second alignment issue arises in the construction of the panel used for the VAR. Bitcoin and ether have a realized volatility on every calendar day, the futures and exchange rates have one on Sunday evenings (computed from a few hours of thin trading) but not on Saturdays, and the VIX has one only on CBOE trading days. The panel used in this version comprises the trading days on which all ten instruments have an own realized volatility computed from their own bars, which in practice is the CBOE calendar: 2{,}514 days from 11 March 2016, the first day with ether data, to 11 March 2026. No value is forward-filled, and Saturday and Sunday crypto volatility does not enter the baseline. The May 2026 version instead built a panel on all 3{,}651 calendar days of the same period, filling missing values forward for up to five days; 1{,}044 of its rows were weekends and 1{,}137 contained at least one forward-filled value, so that on more than 30\% of the observations eight of the ten series had, by construction, zero innovation. \Cref{sec:appendix_audit} quantifies the consequences. As a robustness check we also use a weekend-inclusive crypto measure, in which the realized variance of bitcoin and ether on a trading day is the average daily variance over the calendar days elapsed since the previous trading day, so that Monday carries Saturday and Sunday information. | |
| 45 | + | |
| 46 | +\subsection{Descriptive Statistics of 5-Minute Returns} | |
| 47 | + | |
| 48 | +\Cref{tab:descriptive_stats} summarizes the 5-minute log returns over each instrument's full history. Returns more than twenty sample standard deviations from the mean were removed before computing realized volatility, as a guard against data errors; the symmetric bounds in the minimum and maximum columns are the trace of this filter, which removes a very small number of observations but may also remove genuine extreme moves on crash days, a limitation discussed in \Cref{sec:limitations}. Three patterns stand out. Cryptocurrencies and the VIX have 5-minute standard deviations an order of magnitude larger than equity futures and exchange rates (0.60--0.69\% against 0.03--0.08\%), with crude oil the most volatile traditional asset (0.15\%). All distributions are heavy-tailed, with excess kurtosis between 20 and 63. Skewness is small and negative for equity futures and crude oil, small and positive for the exchange rates and the cryptocurrencies, and clearly positive for the VIX ($+1.00$), whose 5-minute changes are dominated by upward jumps. | |
| 43 | 49 | |
| 44 | 50 | \begin{table}[htbp] |
| 45 | 51 | \centering |
| 46 | −\caption{Descriptive Statistics of 5-Minute Log Returns.} | |
| 52 | +\caption{Descriptive statistics of 5-minute log returns.} | |
| 47 | 53 | \label{tab:descriptive_stats} |
| 54 | +\adjustbox{max width=\textwidth}{% | |
| 48 | 55 | \begin{threeparttable} |
| 49 | −\begin{adjustbox}{max width=\textwidth} | |
| 50 | 56 | \begin{tabular}{@{}llr@{\quad}l@{\quad}lrrrr@{\quad}r@{}} |
| 51 | 57 | \toprule |
| 52 | 58 | Asset & Class & $N$ (M) & Start & End & Std (\%) & Skew & Kurt & Min (\%) & Max (\%) \\ |
@@ -63,29 +69,38 @@ ETH & Crypto & 1.01 & 2016-03 & 2026-03 & 0.597 & $+0.03$ & 63.0 & $-12.6 | ||
| 63 | 69 | VIX & Volatility & 0.55 & 2008-01 & 2026-03 & 0.688 & $+1.00$ & 52.6 & $-14.58$ & 14.65 \\ |
| 64 | 70 | \bottomrule |
| 65 | 71 | \end{tabular} |
| 66 | −\end{adjustbox} | |
| 67 | 72 | \begin{tablenotes}[flushleft] |
| 68 | 73 | \footnotesize |
| 69 | −\item \textit{Notes:} Descriptive statistics for 5-minute log returns $r_{i,t,j} = \ln(P_{i,t,j}/P_{i,t,j-1})$. $N$~is the total number of observations in millions. Std~is the standard deviation. Skew~is the skewness. Kurt~is the excess kurtosis. All values in percentage points except $N$. | |
| 74 | +\item \textit{Notes:} 5-minute log returns $r_{i,t,j}$ over each instrument's full history after removal of returns exceeding twenty sample standard deviations in absolute value. $N$ is in millions of observations; Std is the standard deviation; Kurt is excess kurtosis. Std, Min and Max are in percent. Source: \path{results/table1_descriptive_stats.csv}. | |
| 70 | 75 | \end{tablenotes} |
| 71 | −\end{threeparttable} | |
| 76 | +\end{threeparttable}} | |
| 72 | 77 | \end{table} |
| 73 | 78 | |
| 74 | −Several patterns emerge. First, there is a clear hierarchy in return volatility: cryptocurrencies (BTC: 0.648\%, ETH: 0.597\%) and VIX (0.688\%) exhibit an order of magnitude higher 5-minute return volatility compared to equity futures (ES: 0.073\%, NQ: 0.084\%) and FX pairs (EURUSD: 0.032\%). Crude oil (CL: 0.150\%) is the most volatile among traditional assets. Second, all return distributions exhibit substantial excess kurtosis, ranging from 20.4 (EURUSD) to 63.0 (ETH), indicating heavy tails far in excess of the normal distribution. Third, skewness patterns differ systematically: equity futures and crude oil exhibit slight negative skewness (leverage effects), VIX displays pronounced positive skewness ($+1.00$), and cryptocurrency returns are approximately symmetric. | |
| 75 | − | |
| 76 | −\subsection{Realized Volatility Construction} | |
| 79 | +\subsection{Daily Realized Volatility} | |
| 77 | 80 | |
| 78 | −We compute daily realized volatility for each asset using Equations~\eqref{eq:rv} and~\eqref{eq:rv_annualized}, requiring a minimum of 20 intraday observations per day. \Cref{fig:rv_timeseries} displays the time series of annualized daily realized volatility for all 10 assets. | |
| 81 | +\Cref{fig:rv_timeseries} plots the annualized daily realized volatility of the ten instruments over their full histories, and \Cref{tab:rv_descriptives} summarizes the series over the common 2016--2026 trading-day panel. Mean annualized realized volatility ranges from 7\% for EUR/USD to 34\% for crude oil among traditional assets, and exceeds 100\% for bitcoin, ether and the VIX. The medians are far below the means for the cryptocurrencies (53\% against 103\% for bitcoin), a sign of the extreme right tail: the largest bitcoin values, above 1{,}000\% annualized, occur in April--May and December 2017 and reflect 5-minute prices that oscillated by 5--10\% between consecutive bars on a composite feed of exchanges with large and shifting premia; we verified on an independent one-minute feed from the same vendor that these values are a property of the source data and not of our processing. Skewness in levels is between 1.9 and 5.9; after the log transformation it falls to between 0.2 and 1.4 and excess kurtosis to between 0.1 and 4.0. Log realized volatility is strongly persistent, with first-order autocorrelations between 0.55 (VIX) and 0.91 (BTC) and autocorrelations at lag 22 between 0.12 and 0.66. Augmented Dickey--Fuller tests reject a unit root at the 1\% level for all series except ether (5\%), while KPSS tests reject level stationarity for all series except EUR/USD; the combination is the familiar signature of long memory in realized volatility \citep{Andersen2003,Corsi2009}, which a finite-order VAR approximates rather than reproduces. | |
| 79 | 82 | |
| 80 | 83 | \begin{figure}[htbp] |
| 81 | 84 | \centering |
| 82 | 85 | \includegraphics[width=\textwidth]{fig1_rv_timeseries.png} |
| 83 | −\caption{Daily Realized Volatility Time Series (Annualized, 5-Minute Frequency).} | |
| 86 | +\caption{Daily annualized realized volatility, 2008--2026.} | |
| 84 | 87 | \label{fig:rv_timeseries} |
| 85 | 88 | \begin{minipage}{0.95\textwidth} |
| 86 | 89 | \vspace{4pt} |
| 87 | −\footnotesize\textit{Notes:} Each panel displays the annualized daily realized volatility $\sigma_{i,t}^{\RV} = \sqrt{252 \cdot \sum_{j} r_{i,t,j}^2}$ for one asset. Note the different $y$-axis scales across panels. The COVID-19 crash (March 2020) generates the most prominent volatility spike across all traditional assets. | |
| 90 | +\footnotesize\textit{Notes:} Annualized realized volatility $\sigma_{i,t} = \sqrt{252 \sum_j r_{i,t,j}^2}$ from 5-minute returns, Eastern-time calendar days with at least 20 bars. The $y$-axis scale differs across panels. The March 2020 spike is visible in every traditional asset; the 2017 spikes in bitcoin and ether reflect the quality of the composite spot feed in that year (see text). | |
| 88 | 91 | \end{minipage} |
| 89 | 92 | \end{figure} |
| 90 | 93 | |
| 91 | −The mean annualized realized volatilities are: ES~(13.85\%), NQ~(16.40\%), EURUSD~(6.96\%), USDJPY~(7.71\%), GBPUSD~(7.16\%), GC~(14.00\%), CL~(29.67\%), BTC~(98.69\%), ETH~(110.58\%), and VIX~(105.96\%). | |
| 94 | +\begin{table}[htbp] | |
| 95 | +\centering | |
| 96 | +\caption{Daily realized volatility over the common trading-day panel, 2016-03-11 to 2026-03-11.} | |
| 97 | +\label{tab:rv_descriptives} | |
| 98 | +\adjustbox{max width=\textwidth}{% | |
| 99 | +\begin{threeparttable} | |
| 100 | +\input{tables/tab_rv_descriptives} | |
| 101 | +\begin{tablenotes}[flushleft] | |
| 102 | +\footnotesize | |
| 103 | +\item \textit{Notes:} $T = 2{,}514$ trading days. Mean, median and maximum of annualized realized volatility in percent. Skewness in levels and skewness, excess kurtosis and first-order autocorrelation $\rho_1$ of log realized volatility. ADF is the augmented Dickey--Fuller statistic with a constant and AIC-selected lags (\sym{***}, \sym{**}: rejection of a unit root at 1\% and 5\%; all series reject at 1\% except ETH, $p = 0.04$). KPSS is the level-stationarity statistic with automatic bandwidth; \sym{*} marks rejection of stationarity at the 5\% level. Source: \path{results/rev_table_rv_descriptives.csv}. | |
| 104 | +\end{tablenotes} | |
| 105 | +\end{threeparttable}} | |
| 106 | +\end{table} | |
modified
paper/sections/discussion.tex
+16 −9
@@ -3,22 +3,29 @@ | ||
| 3 | 3 | \label{sec:discussion} |
| 4 | 4 | % ============================================================================ |
| 5 | 5 | |
| 6 | −\subsection{Addressing the Research Questions} | |
| 6 | +\subsection{Answers to the Research Questions} | |
| 7 | 7 | |
| 8 | −\paragraph{RQ1: Intraday volatility propagation.} Our analysis reveals a clear hierarchical structure in cross-asset volatility propagation. U.S.\ equity index futures serve as the primary volatility transmitters, with combined net spillovers exceeding $+46\%$. Volatility propagates outward from equities to FX (particularly EURUSD), commodities, and the VIX. Crypto markets remain largely insulated, with own-shock contributions exceeding 77\%. The total spillover index of 55.44\% underscores the limitations of single-asset volatility models. | |
| 8 | +\paragraph{Structure of connectedness.} Cross-asset shocks explain 54.8\% of the ten-day forecast-error variance of log realized volatility, an estimate that is stable across lag orders, horizons and the treatment of weekend crypto variance (53.7--55.5\%) and whose bootstrap interval is about four percentage points wide. The hierarchy has three robust elements: the two equity index futures are the only net transmitters whose intervals exclude zero in the full sample and in every robustness specification; the realized volatility of the VIX, crude oil and sterling are robust net receivers; and the remaining instruments---the euro, the yen, gold, bitcoin and ether---have net positions that cannot be distinguished from zero over the decade. This ordering is consistent with the primacy of U.S. equities found by \citet{DieboldYilmaz2012} for stocks, bonds, exchange rates and commodities, and it adds two observations: the realized volatility of an implied-volatility index behaves as a derivative of its underlying, and crude oil, often cast as a source of macroeconomic volatility, has been a receiver of equity-market volatility over 2016--2026. | |
| 9 | 9 | |
| 10 | −\paragraph{RQ2: Regime dependence.} The magnitude, direction, and speed of volatility transmission vary dramatically across regimes. Three patterns emerge: (i)~in tranquil periods, equity futures dominate (ES net: $+76.4\%$ pre-COVID); (ii)~during acute crises, safe-haven currencies assume the transmitter role (USDJPY: $+60.3\%$ during COVID); (iii)~during macro-driven regimes, transmission becomes more distributed (EURUSD: $+9.5\%$, BTC: $+7.9\%$ during 2022). The TSI itself is less responsive to regime shifts (64.7\%--66.7\%) than the directional composition, suggesting that ``who transmits to whom'' is more informative than ``how much total transmission occurs.'' | |
| 10 | +\paragraph{Regime dependence.} The total index varies much less across regimes (59.9--71.7\%) than the directional composition. The COVID-19 crash is the only sub-sample in which an instrument other than the equity futures takes the lead, USD/JPY, with a point estimate that is large and a sign that is established but a magnitude that the data cannot pin down ($+7$ to $+135$ percentage points). The statement in the earlier version that equity futures became net receivers during the crash is not supported once sampling uncertainty is taken into account; nor is the statement that bitcoin became a net transmitter during the 2022 tightening cycle. What the regime analysis establishes with confidence is more modest: the hierarchy is dominated by equities in calm and macro-driven periods, exchange-rate volatility became the common factor during the dollar funding squeeze of March 2020, and in the most recent period bitcoin and ether are net receivers. | |
| 11 | 11 | |
| 12 | −\paragraph{RQ3: Volatility hierarchy and crypto integration.} The full-sample hierarchy is: ES~($+26.8$) $>$ NQ~($+19.7$) $>$ BTC~($+1.2$) $>$ EURUSD~($+0.4$) $>$ ETH~($-1.0$) $>$ GC~($-2.9$) $>$ USDJPY~($-5.0$) $>$ CL~($-7.2$) $>$ GBPUSD~($-8.7$) $>$ VIX~($-23.4$). BTC's transition from neutral/receiver to significant transmitter ($+7.9\%$ during rate hikes) represents a structural shift, consistent with institutional adoption and spot Bitcoin ETF approvals. | |
| 12 | +\paragraph{Crypto integration and its direction.} Integration has increased, and in a well-defined sense. The share of bitcoin's forecast-error variance explained by traditional instruments rose from below 10\% in 2017 and 2019 to 20--34\% in 2020--2024 and 46\% in 2025, bitcoin's own share fell from 78\% before 2020 to 48\% after, and the pairwise shares with ES grew in both directions. The direction of net transmission, however, runs from equities to crypto: bitcoin's net spillover is negative in every calendar year since 2020 and significantly so in the spot-ETF period, its 500-day rolling net spillover has been negative since 2022, and the session-ordered regressions show that the U.S.-session volatility of ES, NQ and the VIX predicts bitcoin's next Asian-session volatility whereas bitcoin's overnight and weekend volatility does not predict U.S.-session equity volatility. The one exception, a small but significant predictive effect of bitcoin's earlier-session volatility on the U.S.-session volatility of the VIX, is consistent with option markets pricing overnight risk-asset news before the cash open rather than with crypto volatility originating shocks. These results align with the post-2020 increase in crypto--equity comovement documented by \citet{Iyer2022} and \citet{Elsayed2022} and with the finding of \citet{ConlonMcGee2020} that bitcoin did not act as a safe haven in March 2020, and they qualify the interpretation of growing integration as growing influence: the volatility of the two largest cryptocurrencies has become more exposed to the traditional system, not the reverse. | |
| 13 | 13 | |
| 14 | −\paragraph{RQ4: Systemic risk indicator.} The rolling TSI demonstrates potential as a systemic risk monitor: (i)~it rises \textit{before} major events (the 200-day window captures gradual dependency buildups); (ii)~the maximum (81.55\%, February 2018) precedes the Volmageddon episode; (iii)~it correctly identifies the 2022 rate-hiking cycle as elevated systemic risk. However, the rolling window introduces smoothing that can delay detection of rapid shifts. | |
| 14 | +\paragraph{Time variation.} Total connectedness fell to its minimum during the 2017 crypto boom, rose sharply during the COVID-19 crash and again during the 2022 tightening cycle, and reached the highest values of the sample in 2025, when the calendar-year estimate was 71.5\% against 51--55\% in 2016--2019. Whether the 2025 level reflects a lasting change in market structure---the integration of crypto through exchange-traded funds, the growth of volatility-targeting and option-selling strategies---or the particular shocks of that year cannot be settled with one year of data. We refrain from interpreting the rolling index as an early-warning indicator: in the trading-day panel it does not rise ahead of the March 2020 crash, and the February 2018 spike that motivated this interpretation in the earlier version was an artefact of forward-filled observations. | |
| 15 | 15 | |
| 16 | −\paragraph{RQ5: Trading session differences.} Equity futures and VIX concentrate volatility during European and U.S.\ hours, with the European session generating the highest volatility for both ES (0.060\%) and NQ (0.073\%). Bitcoin's near-uniform volatility across sessions (0.245\%--0.266\%) reflects its 24/7 market structure. Granger causality confirms the primacy of equity futures in driving VIX ($F = 19.86$) and the causal independence of Bitcoin. | |
| 16 | +\paragraph{Intraday distribution and sessions.} Equity-futures volatility is concentrated in the U.S. cash session, which generates 53--54\% of daily variance, with the familiar peaks at the open and before the close; the realized volatility of the VIX is even more concentrated (63\%). Bitcoin's volatility is nearly uniform across the 24 hours, with a peak-to-trough ratio of 1.2 and a mild hump in U.S. hours, and weekends carry 22\% of weekly variance. Round-the-clock trading does not translate into round-the-clock information for equity markets: once Friday's volatility is accounted for, the volatility of bitcoin over the weekend carries no incremental information about the volatility of ES on Monday. | |
| 17 | 17 | |
| 18 | −\subsection{Implications for Portfolio Construction and Risk Management} | |
| 18 | +\subsection{Comparison with the Literature and Implications} | |
| 19 | 19 | |
| 20 | −Our findings carry several practical implications. First, the documented spillover asymmetries complicate cross-asset hedging: VIX instruments respond to equity shocks rather than providing independent signals. Second, the growing crypto--traditional integration during the 2022 rate-hiking period suggests diminishing diversification benefits of crypto allocation precisely when diversification is most needed. Third, the session-dependent nature of volatility transmission implies that risk limits could be optimized by trading session, with tighter controls during the European--U.S.\ overlap. | |
| 20 | +The connectedness level of 55\% is within the range reported for daily volatility systems of comparable size \citep{DieboldYilmaz2012,DieboldYilmaz2014}, and the dominance of equity futures matches most multi-asset applications. Our crypto results sit between the early finding of isolation \citep{Corbet2018,Baur2018} and the post-pandemic finding of integration \citep{Iyer2022}: the gross linkages have grown, the net direction is from equities to crypto, and the within-crypto block remains the dominant source of crypto variance, as in \citet{Ji2019a}. The intraday results confirm, with ten years of 5-minute data, the U-shaped equity pattern of \citet{Wood1985} and \citet{Harris1986} and the U.S.-hours hump in bitcoin volatility of \citet{Eross2019}. | |
| 21 | + | |
| 22 | +For practitioners, three implications follow. The realized volatility of VIX-linked instruments responds to equity-futures volatility rather than anticipating it, so that positions in VIX products are not an independent source of volatility information at the daily frequency. The diversification benefit of cryptocurrencies has eroded in the volatility dimension since 2020 and is smallest in the most recent period, precisely when equity volatility is high. And because equity-futures variance is concentrated in the U.S. cash session while bitcoin's is spread evenly, risk limits that are calibrated on daily volatility understate the intraday concentration of equity risk and overstate that of crypto risk. | |
| 23 | + | |
| 24 | +\subsection{Methodological Lessons} | |
| 25 | + | |
| 26 | +Two methodological conclusions apply beyond this paper. First, in panels that mix 24/7 and exchange-traded instruments, the construction of the trading calendar is a modelling decision with first-order consequences: forward-filling the exchange-traded series over weekends changes the total index by five percentage points, the net spillover of ES by fifteen, and the apparent isolation of the crypto block from a cross-asset share of 6\% to one below 1\% (\Cref{sec:appendix_audit}). Second, connectedness estimates from short windows are imprecise: a ten-variable VAR(4) has 41 coefficients per equation, and in windows of 85--300 observations the 90\% intervals of net spillovers are 30--130 percentage points wide. Regime narratives built on the sign of such estimates, including some in the earlier version of this paper, do not survive the addition of confidence intervals. Time-varying-parameter VARs \citep{Antonakakis2020} or shrinkage estimators would be natural ways to recover time variation with fewer effective parameters. | |
| 21 | 27 | |
| 22 | 28 | \subsection{Limitations} |
| 29 | +\label{sec:limitations} | |
| 23 | 30 | |
| 24 | −Several limitations merit acknowledgment. First, the realized volatility measure based on 5-minute returns may be affected by microstructure noise during illiquid periods. Second, the VAR(4) model imposes a linear structure that may not fully capture nonlinear and asymmetric spillovers during extreme events. Third, the 200-day rolling window involves a trade-off between responsiveness and estimation precision. Fourth, the Granger causality analysis uses daily realized volatility without session-specific splitting, reflecting full-sample relationships. Fifth, the selection of 10 assets, while covering the major classes, excludes potentially important instruments such as emerging market currencies, agricultural commodities, and smaller cryptocurrencies. | |
| 31 | +Several limitations remain. The 5-minute realized variance includes jump variation and, for the composite cryptocurrency feeds of 2016--2017, variation that reflects price discrepancies across exchanges rather than fundamental volatility; the results for 2018--2026 are qualitatively unchanged, but a jump-robust estimator \citep{Andersen2007} and a single-exchange price series would be preferable. The filter that removes 5-minute returns beyond twenty standard deviations, applied before realized volatility was computed, may have removed genuine extreme moves on crash days and so understated realized volatility on the days that matter most for connectedness; its effect could not be quantified without re-processing the raw bars. The continuous futures series splice contracts at roll dates and roll returns were not removed. The VAR is linear and symmetric and does not distinguish spillovers from good and bad volatility \citep{Barunik2016,Barunik2017} or across frequencies \citep{Barunik2018}. The residual bootstrap ignores conditional heteroskedasticity in the innovations of log realized volatility and the intervals are therefore indicative. Finally, with ten instruments the system omits sovereign bonds, emerging-market currencies, agricultural commodities and smaller cryptocurrencies, and the ``U.S. equity'' factor identified here may partly stand in for a global risk factor that a broader system would attribute differently. | |
modified
paper/sections/introduction.tex
+7 −13
@@ -3,22 +3,16 @@ | ||
| 3 | 3 | \label{sec:introduction} |
| 4 | 4 | % ============================================================================ |
| 5 | 5 | |
| 6 | −Understanding how volatility propagates across asset classes is fundamental to modern portfolio management, risk assessment, and financial stability monitoring. The interconnectedness of global financial markets has increased substantially over the past two decades, driven by algorithmic trading, cross-border capital flows, exchange-traded funds linking disparate asset classes, and the emergence of cryptocurrency markets as a new store of value. These developments have intensified the channels through which volatility shocks in one market can rapidly transmit to others, raising important questions about the nature, magnitude, and time-varying dynamics of cross-asset volatility spillovers. | |
| 6 | +How volatility propagates from one market to another matters for portfolio construction, for the design of risk limits, and for the monitoring of systemic risk. Over the past two decades the channels of propagation have multiplied: index futures and exchange-traded funds trade almost around the clock, cross-asset strategies rebalance mechanically in response to volatility, and cryptocurrencies have grown from a marginal curiosity into an asset class with a market capitalization in the trillions of dollars and, since January 2024, spot exchange-traded funds listed in the United States. Whether these developments have altered the hierarchy of volatility transmission---which markets originate volatility shocks and which absorb them---is an empirical question, and one whose answer appears to change with the sample period and with the econometric choices made along the way. | |
| 7 | 7 | |
| 8 | −The seminal work of \citet{DieboldYilmaz2009,DieboldYilmaz2012,DieboldYilmaz2014} established a rigorous econometric framework for measuring volatility connectedness based on generalized forecast error variance decompositions from vector autoregressive (VAR) models. This approach decomposes the forecast error variance of each variable into contributions from shocks originating in all variables in the system, providing both aggregate and directional measures of spillovers. Subsequent applications have examined volatility transmission within equities \citep{Demirer2018}, across commodities and equity markets \citep{Kang2017}, and between traditional and crypto assets \citep{Bouri2019,Corbet2020}. | |
| 8 | +The connectedness framework of \citet{DieboldYilmaz2009,DieboldYilmaz2012,DieboldYilmaz2014} offers a transparent way to pose the question. A vector autoregression (VAR) is fitted to a panel of volatilities, and the forecast-error variance of each series at a given horizon is decomposed into the shares attributable to shocks in every series in the system. Aggregating the off-diagonal shares yields a total connectedness index; summing them by row and by column yields the volatility each market receives from, and transmits to, the others. The generalized decomposition of \citet{Koop1996} and \citet{Pesaran1998} makes these quantities invariant to the ordering of the variables, which has made the framework the standard tool for cross-market spillover studies in equities \citep{Demirer2018,DieboldYilmaz2016}, foreign exchange \citep{Barunik2017,GreenwoodNimmo2016}, commodities \citep{Kang2017,Ji2019b} and cryptocurrencies \citep{Ji2019a,Corbet2018}. | |
| 9 | 9 | |
| 10 | −However, several gaps remain in the literature. First, most existing studies rely on daily or weekly data, which may obscure the rapid intraday dynamics of volatility transmission. High-frequency data at the 5-minute level captures the real-time propagation of shocks that daily data aggregates away. Second, the inclusion of cryptocurrency markets---particularly their evolution from isolated speculative instruments to increasingly integrated financial assets---has received limited attention within comprehensive multi-asset connectedness frameworks. Third, the regime-dependent nature of volatility transmission has not been systematically examined across the full spectrum of asset classes using consistent high-frequency data. | |
| 10 | +Three features of the existing evidence motivate this paper. First, most cross-asset studies measure volatility with daily ranges or squared daily returns. Realized volatility computed from intraday returns is a far more precise ex post measure \citep{Andersen2003,BarndorffNielsen2002}, and the precision gain is greatest exactly when connectedness is of most interest, namely on turbulent days. Second, studies that include cryptocurrencies alongside exchange-traded instruments must confront a calendar problem: bitcoin and ether trade every hour of every day, whereas index and commodity futures close for roughly one hour a day and from Friday evening to Sunday evening, and the VIX is disseminated only during Chicago trading hours. How the series are aligned---which days enter the panel, how weekend crypto volatility is treated, and in which time zone the day is defined---is rarely documented, although, as this paper shows, it can shift connectedness estimates by several percentage points and change the sign of net spillovers. Third, point estimates of connectedness are commonly reported without confidence intervals, and regime comparisons are drawn from sub-samples of a few dozen observations in which a ten-variable VAR is severely over-parameterized. | |
| 11 | 11 | |
| 12 | −This paper addresses these gaps by providing a comprehensive analysis of intraday volatility transmission across four major asset classes---equities, foreign exchange (FX), commodities, and cryptocurrencies---using 5-minute OHLCV data spanning January 2008 to March 2026. We construct daily realized volatility measures for 10 representative instruments and apply the \citet{DieboldYilmaz2012} generalized variance decomposition framework to quantify both static and time-varying spillover dynamics. Specifically, we address the following five research questions: | |
| 12 | +This paper studies ten instruments observed at the 5-minute frequency from January 2008 to March 2026: the E-mini S\&P~500 (ES) and Nasdaq~100 (NQ) futures, the EUR/USD, USD/JPY and GBP/USD exchange rates, gold (GC) and WTI crude oil (CL) futures, spot bitcoin (BTC) and ether (ETH), and the CBOE Volatility Index (VIX). Daily realized volatility is constructed for each instrument from 5-minute log returns, and the connectedness of log realized volatility is estimated on the 2{,}514 trading days common to all ten series, from March 2016 to March 2026, with a VAR(4) and a ten-day forecast horizon. Residual-bootstrap intervals accompany every connectedness measure. The time dimension is explored with rolling windows of 200, 250 and 500 trading days, with four regime sub-samples, and with calendar-year estimates. A second block of analyses exploits the intraday data directly: after an explicit conversion of exchange time stamps to Coordinated Universal Time, it documents the hourly periodicity of absolute returns, the share of daily variance generated in Asian, European and U.S. trading hours, and session-ordered predictive regressions between the realized volatility of equity futures, the VIX and bitcoin. | |
| 13 | 13 | |
| 14 | −\begin{enumerate}[label=\textbf{RQ\arabic*.}, leftmargin=2cm] | |
| 15 | − \item How does intraday realized volatility propagate across equities, currencies, commodities, and crypto markets at the 5-minute frequency? | |
| 16 | − \item Does the speed and magnitude of cross-asset volatility transmission vary across market regimes (\eg, the COVID-19 crash, the 2022 rate-hiking cycle, the crypto winter)? | |
| 17 | − \item Which asset classes act as volatility originators versus receivers, and has this hierarchy shifted over time with the maturation of crypto markets? | |
| 18 | − \item Can a high-frequency VAR/network connectedness model identify systemic risk buildups before major market dislocations? | |
| 19 | − \item How do intraday volatility spillovers between VIX futures, equity index futures (ES, NQ), and Bitcoin futures differ during U.S.\ versus European versus Asian trading hours? | |
| 20 | −\end{enumerate} | |
| 14 | +The paper addresses five questions. (i)~What is the structure of daily realized-volatility connectedness across the four asset classes, and which instruments are robust net transmitters or receivers? (ii)~How does this structure change across market regimes, in particular during the COVID-19 crash and the 2022 monetary tightening? (iii)~Has the integration of bitcoin and ether with traditional markets increased, and in which direction does volatility flow? (iv)~How does aggregate connectedness evolve over time, and how is it related to stress episodes? (v)~How is intraday volatility distributed across trading sessions, and does bitcoin's round-the-clock trading carry information for the volatility of U.S. equity markets? | |
| 21 | 15 | |
| 22 | −Our analysis yields several novel findings. First, U.S.\ equity index futures (E-Mini S\&P 500 and E-Mini Nasdaq 100) are the dominant volatility transmitters in the global system, with net directional spillovers of $+26.80\%$ and $+19.72\%$, respectively. The VIX, often perceived as a barometer of market fear, is in fact a net receiver of volatility shocks ($-23.37\%$), absorbing rather than originating cross-asset volatility. Second, the total spillover index exhibits substantial time variation, ranging from 57.22\% to 81.55\%, with sharp increases preceding and during market stress episodes. Third, regime analysis reveals dramatic shifts in the volatility hierarchy: during the COVID-19 crash, USD/JPY emerges as the dominant shock originator, consistent with safe-haven demand dynamics, while equity futures flip from transmitters to receivers. Fourth, Bitcoin demonstrates a gradual transition from volatility receiver to originator, particularly evident during the 2022 rate-hiking period, suggesting growing crypto--traditional market integration. Fifth, Bitcoin's intraday volatility pattern is remarkably uniform across global trading sessions, in stark contrast to the session-dependent patterns of equity and VIX markets. | |
| 16 | +The main results are as follows. Cross-asset shocks explain 54.8\% of the ten-day forecast-error variance of log realized volatility (90\% bootstrap interval 53.1--56.9). ES and NQ are the only robust net transmitters, with net directional spillovers of $+36.0$ and $+25.6$ percentage points; the realized volatility of the VIX ($-20.6$), of crude oil ($-14.2$) and of sterling ($-13.2$) are robust net receivers. The VIX result is not a statement about the VIX level---which is a forward-looking price---but about the day-to-day variability of that price, more than one-fifth of which is explained by shocks to the realized volatility of the equity futures from which it is derived. The net positions of bitcoin and ether are statistically indistinguishable from zero in the full sample and in most sub-samples, and the point estimate for bitcoin changes sign across reasonable specifications. The two cryptocurrencies form a tightly linked pair---each explains 27--28\% of the other's variance---whose exposure to traditional assets has grown markedly: shocks to the eight traditional instruments explained less than 10\% of bitcoin's forecast-error variance in 2017 and 2019, between 20\% and 34\% in 2020--2024, and 46\% in 2025. The direction of this integration is from equities to crypto. In the spot-ETF period (January 2024--March 2026) bitcoin is a significant net receiver ($-12.4$ percentage points, interval $-20.4$ to $-2.1$), and in the intraday analysis the U.S.-session volatility of ES predicts bitcoin's next Asian-session volatility, whereas bitcoin's overnight and weekend volatility carry no incremental information for the U.S.-session volatility of ES. Rolling total connectedness rose sharply in March 2020 and reached the highest values of the sample in 2025; a previously reported peak in February 2018 turns out to be an artefact of forward-filled weekend observations. Intraday, equity and VIX volatility concentrate in the U.S. cash session, which generates 53--63\% of daily variance, while bitcoin's hourly profile is nearly flat, with a peak-to-trough ratio of 1.2 against 3.9 for ES. | |
| 23 | 17 | |
| 24 | −The remainder of this paper is organized as follows. \Cref{sec:literature} reviews the relevant literature. \Cref{sec:methodology} describes the econometric framework. \Cref{sec:data} presents the data and realized volatility construction. \Cref{sec:results} reports the empirical results. \Cref{sec:discussion} discusses the findings in the context of the research questions, and \Cref{sec:conclusion} concludes. | |
| 18 | +Relative to the May 2026 version of this paper, the present version corrects the construction of the daily panel, replaces levels by logarithms of realized volatility, adds bootstrap inference and a robustness grid, corrects the time zone of the intraday analysis, and revises the conclusions accordingly; the changes are documented in the appendix and in the revision log that accompanies the replication code. The remainder of the paper is organized as follows. \Cref{sec:literature} reviews the literature. \Cref{sec:methodology} presents the realized-volatility measure, the connectedness framework, the inference procedure and the session analysis. \Cref{sec:data} describes the data, the alignment of the series and the sample. \Cref{sec:results} reports the results, \Cref{sec:discussion} discusses them in relation to the research questions and the literature, and \Cref{sec:conclusion} concludes. | |
modified
paper/sections/literature.tex
+16 −20
@@ -3,38 +3,34 @@ | ||
| 3 | 3 | \label{sec:literature} |
| 4 | 4 | % ============================================================================ |
| 5 | 5 | |
| 6 | −\subsection{Volatility Spillovers and Connectedness} | |
| 6 | +\subsection{From Volatility Spillovers to Connectedness} | |
| 7 | 7 | |
| 8 | −The study of volatility transmission across financial markets has a long intellectual history, beginning with the recognition that volatility clusters \citep{Mandelbrot1963,Fama1965} and exhibits contagion effects across markets \citep{King1990,Forbes2002}. Early approaches relied on multivariate GARCH models \citep{Engle2002,Baele2005} and regime-switching frameworks \citep{Ang2002} to capture cross-market volatility dynamics. While these models provided important insights, they were limited in their ability to decompose directional spillovers and identify which markets serve as net transmitters versus receivers. | |
| 8 | +The transmission of volatility across markets has been studied since the recognition that large price changes cluster in time \citep{Mandelbrot1963,Fama1965} and that this clustering is correlated across national markets. \citet{Hamao1990} and \citet{Lin1994} documented volatility spillovers between Tokyo, London and New York with univariate and bivariate GARCH models, \citet{King1990} interpreted cross-market transmission as the outcome of rational agents inferring information from foreign price changes, \citet{Longin2001} showed that the correlation of international equity returns rises in bear markets but not in bull markets, and \citet{Forbes2002} showed that measured increases in cross-market correlation during crises are largely a mechanical consequence of higher variance rather than evidence of contagion. Multivariate GARCH specifications, in particular the dynamic conditional correlation model of \citet{Engle2002} and the regime-switching frameworks of \citet{Ang2002} and \citet{Baele2005}, made it possible to track time-varying comovement in moderately sized systems. These approaches, however, describe comovement rather than direction: they do not say which market originates a volatility shock and which absorbs it. | |
| 9 | 9 | |
| 10 | −The introduction of the \citet{DieboldYilmaz2009} spillover index marked a methodological breakthrough. Building on the concept of forecast error variance decompositions from VAR models, they proposed a single summary measure---the total spillover index---that captures the proportion of total forecast error variance attributable to cross-market shocks. \citet{DieboldYilmaz2012} refined this framework by adopting the generalized VAR approach of \citet{Koop1996} and \citet{Pesaran1998}, which eliminates the sensitivity to variable ordering inherent in Cholesky decompositions. This generalized framework yields an asymmetric connectedness matrix that provides directional ``TO'' and ``FROM'' spillover measures for each variable, as well as net directional spillovers. | |
| 10 | +\citet{DieboldYilmaz2009} proposed to answer that question with the forecast-error variance decomposition of a VAR fitted to volatilities. The share of market $i$'s forecast-error variance attributable to shocks in market $j$ is a natural measure of the spillover from $j$ to $i$, and the aggregate of all cross-market shares is a single index of connectedness. Because Cholesky decompositions depend on the ordering of the variables, \citet{DieboldYilmaz2012} adopted the generalized decomposition of \citet{Koop1996} and \citet{Pesaran1998}, which allows for contemporaneously correlated shocks and delivers an asymmetric connectedness table from which directional ``to'', ``from'' and net spillovers follow directly. \citet{DieboldYilmaz2014} reinterpreted the table as a weighted directed network, so that total connectedness is the mean degree of the network and net pairwise spillovers are its signed edges. In their application to four U.S. asset classes, \citet{DieboldYilmaz2012} found that equity volatility transmits to bonds, exchange rates and commodities, and that connectedness rises in crises; this ordering of equities at the top of the hierarchy recurs in most subsequent studies. | |
| 11 | 11 | |
| 12 | −\citet{DieboldYilmaz2014} further extended the methodology to enable network visualization of the connectedness structure, drawing on tools from graph theory. Their approach has since been applied extensively across financial markets: \citet{Demirer2018} examined global bank stock return and volatility connectedness, \citet{Barunik2018} proposed a frequency-domain decomposition of connectedness to distinguish short-run from long-run spillovers, and \citet{Antonakakis2020} applied time-varying parameter (TVP) VAR models to capture smooth evolution of connectedness without the need for rolling windows. | |
| 12 | +The framework has since been extended in several directions. \citet{Barunik2018} decompose connectedness by frequency to separate short-run from long-run transmission; \citet{Barunik2016,Barunik2017} distinguish spillovers generated by negative and positive returns in equity and foreign-exchange markets; \citet{Antonakakis2020} replace rolling-window VARs with time-varying-parameter VARs that do not discard observations; and \citet{Lastrapes2021} propose a joint spillover index that corrects the row normalization of the generalized decomposition. Statistical inference for connectedness measures has received comparatively little attention. Most applications report point estimates, although the measures are smooth functions of VAR parameters whose sampling uncertainty can be approximated by the bootstrap methods developed for impulse responses \citep{Kilian1998,KilianLutkepohl2017}. | |
| 13 | 13 | |
| 14 | −\subsection{Cross-Asset Volatility Transmission} | |
| 14 | +\subsection{Cross-Asset Transmission: Exchange Rates, Commodities and the VIX} | |
| 15 | 15 | |
| 16 | −A growing body of literature examines volatility transmission across different asset classes, motivated by the observation that cross-asset correlations tend to increase during market stress \citep{Longin2001,Ang2002}. \citet{Kang2017} investigated spillovers between commodity and equity markets, finding that oil and gold serve as significant volatility transmitters during crisis periods. \citet{Diebold2012} studied connectedness among four major asset classes and found that return spillovers are more important than volatility spillovers for most market pairs. | |
| 16 | +Within foreign exchange, \citet{GreenwoodNimmo2016} apply the connectedness framework to the G10 currencies and find that risk spillovers intensify in stress episodes, while \citet{Barunik2017} show that negative-return volatility dominates transmission among the major pairs. The yen's behaviour in crises is central to the present paper's regime results: \citet{Ranaldo2010} and \citet{Habib2012} document that the yen and the Swiss franc appreciate when global risk aversion rises, so that USD/JPY volatility reflects the unwinding of carry positions rather than idiosyncratic Japanese news. | |
| 17 | 17 | |
| 18 | −The foreign exchange market, as the world's largest and most liquid financial market, has been shown to play a central role in cross-asset volatility transmission. \citet{Greenwood2014} documented that carry trade unwinds can generate volatility spillovers from FX to equity markets, while \citet{Barunik2016} found significant volatility transmission between the EUR/USD exchange rate and European equity indices. The Japanese yen, as a traditional safe-haven currency, has been shown to exhibit distinctive volatility dynamics during crisis periods \citep{Ranaldo2010,Habib2012}. | |
| 18 | +For commodities, \citet{Arouri2011} and \citet{Mensi2013} document volatility spillovers between crude oil and equity markets and between commodities and equities more generally, \citet{Kang2017} measure spillovers among crude oil, precious metals and agricultural futures and find that they intensify in crises, \citet{Vivian2012} identify structural breaks in commodity volatility, and \citet{Baur2010} and \citet{Reboredo2013} characterize gold as a safe haven for equities and as a hedge for the U.S. dollar. Whether these roles translate into gold being a net receiver or a net transmitter of realized-volatility shocks is an empirical matter addressed below. | |
| 19 | 19 | |
| 20 | −Commodity markets, particularly crude oil and gold, have been extensively studied as both shock transmitters and hedging instruments. \citet{Vivian2012} found significant time-varying volatility spillovers between oil and stock markets across multiple countries. \citet{Baur2010} established gold's role as a safe haven during extreme equity market downturns, while \citet{Reboredo2013} documented asymmetric spillovers between gold and oil prices. | |
| 20 | +The VIX requires a distinct interpretation. It is the risk-neutral expectation of 30-day S\&P~500 variance implied by option prices \citep{Whaley2009}, and its level is closely related to, but systematically above, realized variance, the gap being the variance risk premium \citep{BekaertHoerova2014}. The present paper does not include the VIX level in the VAR; it includes the realized volatility of 5-minute changes in the VIX, that is, the variability of the implied-volatility price itself. The finding that this series is a net receiver of shocks from equity-futures realized volatility is therefore consistent with the VIX being a derivative of the S\&P~500 and does not contradict the predictive content of the VIX level for future realized variance. | |
| 21 | 21 | |
| 22 | −\subsection{Cryptocurrency and Traditional Market Integration} | |
| 22 | +\subsection{Cryptocurrencies and Traditional Markets} | |
| 23 | 23 | |
| 24 | −The emergence of cryptocurrency markets has introduced a new dimension to cross-asset volatility analysis. Early studies found limited connectedness between Bitcoin and traditional financial assets \citep{Bouri2017,Corbet2018}, supporting the diversification benefits of including crypto in multi-asset portfolios. However, more recent evidence suggests increasing integration, particularly during market stress periods. | |
| 24 | +Early studies found cryptocurrencies to be largely detached from traditional asset classes. \citet{Bouri2017} conclude that bitcoin is a diversifier rather than a hedge or a safe haven, \citet{Corbet2018} find that connectedness between cryptocurrencies and conventional assets is weak and concentrated within the crypto group, and \citet{Baur2018} show that bitcoin returns are essentially uncorrelated with those of traditional assets. The within-crypto dependence is strong: \citet{Ji2019a} document a dense connectedness network among the largest coins, and \citet{Makarov2020} attribute part of the common dynamics to arbitrage across exchanges. Bitcoin's volatility is also unusual in level and dynamics: \citet{Katsiampa2017} and \citet{Chaim2018} document pronounced jump components, which is relevant for the choice between levels and logarithms of realized volatility in a VAR. | |
| 25 | 25 | |
| 26 | −\citet{Bouri2019} examined volatility spillovers between Bitcoin and a range of financial assets, finding that crypto--traditional market connectedness increased significantly after 2017. \citet{Corbet2020} analyzed the contagion dynamics between cryptocurrencies and conventional financial markets during the COVID-19 pandemic, documenting a sharp increase in crypto--equity correlations. \citet{Yousaf2022} extended this analysis to include a broader set of cryptocurrencies and found evidence of increasing volatility transmission from crypto to commodity markets. | |
| 26 | +The COVID-19 episode changed the assessment. \citet{ConlonMcGee2020} find that bitcoin lost value together with equities in March 2020 and did not act as a safe haven, \citet{Bouri2020} find with wavelet methods that neither bitcoin nor gold and commodities offered reliable safe-haven protection for equities at short horizons, \citet{Corbet2020} document contagion from equities to gold and cryptocurrencies, and \citet{Elsayed2022} report increased risk transmission between bitcoin and traditional assets during the pandemic. \citet{Iyer2022} shows that the correlation of bitcoin returns with U.S. equity returns and the share of equity-volatility variance explained by crypto shocks both rose after 2020, and relates the change to the entry of institutional investors. Studies of cryptocurrency--commodity links \citep{Ji2019b} and of meme assets \citep{Yousaf2023} point in the same direction of growing but still modest integration. Whether the direction of transmission has shifted---whether crypto volatility now originates shocks that reach traditional markets, or mainly absorbs them---remains open, and the sign of bitcoin's net spillover reported in the literature varies with the sample and the specification. The present paper addresses this question with confidence intervals, calendar-year estimates and session-ordered predictive regressions. | |
| 27 | 27 | |
| 28 | −The question of whether crypto markets have transitioned from volatility receivers to originators has important implications for systemic risk monitoring. \citet{Ante2021} provided evidence of Bitcoin's growing influence on traditional markets, particularly through the channel of institutional adoption and the introduction of crypto-linked exchange-traded products. More recently, \citet{Makarov2020} documented the role of arbitrage and cross-exchange price discovery in the crypto market microstructure. | |
| 28 | +\subsection{Realized Volatility and Intraday Periodicity} | |
| 29 | 29 | |
| 30 | −\subsection{Intraday Volatility Dynamics and Trading Sessions} | |
| 30 | +Realized volatility, the sum of squared intraday returns, is a consistent estimator of the integrated variance of a continuous-time price process as the sampling interval shrinks \citep{Andersen2001,Andersen2003,BarndorffNielsen2002}. At very fine sampling intervals, however, bid--ask bounce and discreteness introduce a bias that grows with the number of observations \citep{HansenLunde2006,AitSahalia2005,Zhang2005}. In a comparison of hundreds of realized measures across asset classes, \citet{Liu2015} find that it is difficult to improve significantly on 5-minute realized variance, which justifies the sampling frequency used here. The logarithm of realized volatility is close to normally distributed and strongly persistent \citep{Andersen2003}, a persistence that the heterogeneous autoregressive model of \citet{Corsi2009} captures parsimoniously, and realized measures are themselves estimated with error, with consequences for the dynamics of volatility models \citep{Bollerslev2016}. Jumps add a further component to realized variance that can be separated with bipower variation \citep{Andersen2007}. | |
| 31 | 31 | |
| 32 | −The use of high-frequency data to study volatility dynamics has a rich tradition in financial econometrics. \citet{Andersen2001,Andersen2003} pioneered the use of realized volatility constructed from intraday returns as a model-free measure of ex post volatility. The optimal sampling frequency for realized volatility estimation has been debated extensively, with \citet{BarndorffNielsen2002} and \citet{Zhang2005} addressing the trade-off between discretization bias and microstructure noise. | |
| 32 | +Intraday volatility follows strong deterministic patterns: equity volatility is highest at the open and the close of the cash session \citep{Wood1985,Harris1986}, and the periodicity in exchange-rate volatility tracks the opening hours of the Asian, European and American centres and the release times of macroeconomic announcements \citep{Andersen1997,Andersen1998}. For bitcoin, \citet{Eross2019} find that volatility and volume are highest during U.S. trading hours despite continuous trading, and \citet{Baur2019} document time-of-day and day-of-week effects in returns and volume, with lower activity at weekends. These patterns bear on the alignment problem studied here: a ``day'' of volatility means different things for a market that closes and for one that does not. | |
| 33 | 33 | |
| 34 | −Intraday volatility patterns exhibit well-documented regularities across asset classes. Equity markets display a U-shaped or reverse J-shaped intraday volatility pattern, with elevated volatility at the open and close of trading \citep{Wood1985,Harris1986}. FX markets, trading 24 hours, show volatility peaks during the overlap of major trading sessions \citep{Andersen1998}. Cryptocurrency markets, as continuously traded assets, display distinctive intraday patterns that reflect their global, decentralized nature \citep{Eross2019}. | |
| 34 | +\subsection{Contribution} | |
| 35 | 35 | |
| 36 | −The interaction between trading sessions has been studied primarily in the context of equity markets. \citet{Hamao1990} found evidence of volatility spillovers from the Tokyo Stock Exchange to London and New York, while \citet{Lin1994} documented bidirectional volatility transmission between the New York and Tokyo stock markets. More recently, \citet{Fry2022} examined how Bitcoin's 24/7 trading provides a continuous information channel that can bridge traditional market close-to-open gaps. | |
| 37 | − | |
| 38 | −\subsection{Contribution to the Literature} | |
| 39 | − | |
| 40 | −This paper contributes to the existing literature in several important ways. First, we provide the most comprehensive high-frequency multi-asset connectedness analysis to date, spanning four asset classes with 5-minute data over an 18-year period. Second, we document the time-varying evolution of the volatility transmitter--receiver hierarchy, with particular attention to the changing role of cryptocurrency markets. Third, we exploit the 24/7 nature of crypto trading to examine session-specific volatility spillovers, providing novel evidence on the role of trading hours in shaping cross-asset volatility dynamics. Fourth, we demonstrate that the Diebold--Yilmaz connectedness framework, applied at high frequency, can serve as an early warning indicator for systemic risk buildups. | |
| 36 | +The paper contributes to this literature in four ways. First, it measures cross-asset connectedness with realized rather than range- or return-based volatility for ten instruments spanning equities, foreign exchange, commodities, implied volatility and cryptocurrencies over a decade that includes the COVID-19 crash, the 2022 tightening cycle and the launch of spot bitcoin ETFs. Second, it treats the alignment of 24/7 and exchange-traded series explicitly and quantifies its effect on the estimates: forward-filling weekend observations, a common but seldom documented practice, alters the total connectedness index by five percentage points and the net spillover of equity futures by fifteen. Third, it attaches bootstrap confidence intervals to all connectedness measures and shows that several widely discussed regime results---including the sign of bitcoin's net spillover---are not statistically distinguishable from zero in sub-samples of the usual size. Fourth, it uses the intraday data not only to construct daily realized volatility but to test, with correctly time-zoned session volatilities, whether bitcoin's overnight and weekend trading carries information for the volatility of U.S. equity futures. | |
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paper/sections/methodology.tex
+79 −59
@@ -4,112 +4,132 @@ | ||
| 4 | 4 | % ============================================================================ |
| 5 | 5 | |
| 6 | 6 | \subsection{Realized Volatility} |
| 7 | +\label{sec:rv} | |
| 7 | 8 | |
| 8 | −We construct daily realized volatility from intraday 5-minute log returns. For asset $i$ on day $t$, let $P_{i,t,j}$ denote the closing price of the $j$-th 5-minute bar, where $j = 1, \ldots, M_t$ and $M_t$ is the number of intraday observations. The 5-minute log return is: | |
| 9 | +For instrument $i$ on calendar day $t$, let $P_{i,t,j}$ denote the closing price of the $j$-th 5-minute bar, $j = 1, \ldots, M_{i,t}$, where $M_{i,t}$ is the number of bars available on that day. The 5-minute log return and the daily realized variance are | |
| 9 | 10 | \begin{equation} |
| 10 | − r_{i,t,j} = \ln\left(\frac{P_{i,t,j}}{P_{i,t,j-1}}\right). | |
| 11 | − \label{eq:logreturn} | |
| 12 | −\end{equation} | |
| 13 | − | |
| 14 | −The daily realized variance is computed as the sum of squared intraday returns \citep{Andersen2003,BarndorffNielsen2002}: | |
| 15 | −\begin{equation} | |
| 16 | − \RV_{i,t} = \sum_{j=1}^{M_t} r_{i,t,j}^2. | |
| 11 | + r_{i,t,j} = \ln P_{i,t,j} - \ln P_{i,t,j-1}, | |
| 12 | + \qquad | |
| 13 | + \RV_{i,t} = \sum_{j=1}^{M_{i,t}} r_{i,t,j}^2 . | |
| 17 | 14 | \label{eq:rv} |
| 18 | 15 | \end{equation} |
| 19 | − | |
| 20 | −The annualized daily realized volatility is then: | |
| 16 | +If the log price is a continuous semimartingale with spot variance $\sigma_{i,t}^2(s)$ and the sampling interval shrinks, $\RV_{i,t}$ converges in probability to the integrated variance $\int_{t-1}^{t} \sigma_{i,t}^2(s)\,ds$ \citep{Andersen2003,BarndorffNielsen2002}; in the presence of jumps it converges to the integrated variance plus the sum of squared jumps \citep{Andersen2007}. At the 5-minute frequency the bias induced by microstructure noise is small for liquid instruments \citep{HansenLunde2006,Liu2015}. We report realized volatility in annualized form, | |
| 21 | 17 | \begin{equation} |
| 22 | − \sigma_{i,t}^{\RV} = \sqrt{252 \cdot \RV_{i,t}}. | |
| 18 | + \sigma_{i,t} = \sqrt{252 \cdot \RV_{i,t}}, | |
| 23 | 19 | \label{eq:rv_annualized} |
| 24 | 20 | \end{equation} |
| 25 | − | |
| 26 | −We impose a minimum threshold of $M_t \geq 20$ intraday observations per day to ensure reliable realized volatility estimation. Days with fewer observations are excluded. Under standard assumptions, as the sampling frequency increases ($M_t \to \infty$), $\RV_{i,t}$ converges to the integrated variance: | |
| 21 | +and require $M_{i,t} \geq 20$ bars for a day to be retained. Because $\sigma_{i,t}$ is strongly right-skewed and heavy-tailed whereas its logarithm is close to Gaussian \citep{Andersen2001,Andersen2003}, the connectedness analysis is conducted on | |
| 27 | 22 | \begin{equation} |
| 28 | − \RV_{i,t} \xrightarrow{p} \int_0^1 \sigma_{i,t}^2(s)\, ds. | |
| 29 | − \label{eq:rv_convergence} | |
| 23 | + y_{i,t} = \ln \sigma_{i,t}, | |
| 24 | + \label{eq:logrv} | |
| 30 | 25 | \end{equation} |
| 31 | − | |
| 32 | −The 5-minute sampling frequency represents a widely accepted compromise between capturing sufficient intraday variation and avoiding microstructure noise contamination \citep{Liu2015}. | |
| 26 | +which is equal to $\tfrac12 \ln \RV_{i,t}$ up to a constant. The transformation matters for the VAR because the generalized variance decomposition weights observations by their squared innovations: in levels, a handful of extreme days dominates the residual covariance matrix, and the decomposition then describes those days rather than the typical transmission mechanism. Results in levels are reported as a robustness check. Stationarity of $y_{i,t}$ is assessed with the augmented Dickey--Fuller test \citep{DickeyFuller1979} and the KPSS test \citep{Kwiatkowski1992}. | |
| 33 | 27 | |
| 34 | 28 | \subsection{Vector Autoregression} |
| 29 | +\label{sec:var} | |
| 35 | 30 | |
| 36 | −Let $\mathbf{y}_t = (\RV_{1,t}, \RV_{2,t}, \ldots, \RV_{N,t})'$ denote the $N \times 1$ vector of daily realized volatilities for $N = 10$ assets. We model the joint dynamics using a VAR($p$) process: | |
| 31 | +Let $\mathbf{y}_t = (y_{1,t}, \ldots, y_{N,t})'$ collect the $N = 10$ log realized volatilities on trading day $t$. The dynamics are approximated by a covariance-stationary VAR($p$), | |
| 37 | 32 | \begin{equation} |
| 38 | 33 | \mathbf{y}_t = \boldsymbol{\mu} + \sum_{\ell=1}^{p} \boldsymbol{\Phi}_\ell \mathbf{y}_{t-\ell} + \boldsymbol{\varepsilon}_t, |
| 34 | + \qquad \mathbb{E}[\boldsymbol{\varepsilon}_t \boldsymbol{\varepsilon}_t'] = \boldsymbol{\Sigma}, | |
| 39 | 35 | \label{eq:var} |
| 40 | 36 | \end{equation} |
| 41 | −where $\boldsymbol{\mu}$ is an $N \times 1$ vector of intercepts, $\boldsymbol{\Phi}_\ell$ are $N \times N$ coefficient matrices, and $\boldsymbol{\varepsilon}_t \sim (0, \boldsymbol{\Sigma})$ is the vector of reduced-form innovations with covariance matrix $\boldsymbol{\Sigma}$. We set $p = 4$ lags throughout. The VAR($p$) admits the moving average representation: | |
| 37 | +estimated equation by equation by least squares \citep{Lutkepohl2005}. The lag order is chosen by comparing the Akaike, Schwarz and Hannan--Quinn criteria over $p \in \{1, \ldots, 10\}$ (\Cref{tab:lag_selection} in the appendix). The criteria select $p = 5$, $3$ and $4$ respectively; we adopt the Hannan--Quinn choice, $p = 4$, which coincides with the original specification of the paper, and report $p \in \{1, 2, 3, 6\}$ as robustness checks. The moving-average representation of \eqref{eq:var} is $\mathbf{y}_t = \boldsymbol{\mu}^{*} + \sum_{h=0}^{\infty} \boldsymbol{\Psi}_h \boldsymbol{\varepsilon}_{t-h}$ with | |
| 42 | 38 | \begin{equation} |
| 43 | − \mathbf{y}_t = \boldsymbol{\mu}^* + \sum_{s=0}^{\infty} \boldsymbol{\Psi}_s \boldsymbol{\varepsilon}_{t-s}, | |
| 44 | − \label{eq:vma} | |
| 45 | −\end{equation} | |
| 46 | −where the $N \times N$ coefficient matrices $\boldsymbol{\Psi}_s$ are computed recursively: | |
| 47 | −\begin{equation} | |
| 48 | − \boldsymbol{\Psi}_s = \sum_{\ell=1}^{p} \boldsymbol{\Phi}_\ell \boldsymbol{\Psi}_{s-\ell}, \quad s = 1, 2, \ldots | |
| 39 | + \boldsymbol{\Psi}_0 = \mathbf{I}_N, | |
| 40 | + \qquad | |
| 41 | + \boldsymbol{\Psi}_h = \sum_{\ell=1}^{\min(h,p)} \boldsymbol{\Phi}_\ell \boldsymbol{\Psi}_{h-\ell}, \quad h \geq 1 . | |
| 49 | 42 | \label{eq:psi_recursion} |
| 50 | 43 | \end{equation} |
| 51 | −with $\boldsymbol{\Psi}_0 = \mathbf{I}_N$ and $\boldsymbol{\Phi}_\ell = \mathbf{0}$ for $\ell > p$. | |
| 52 | 44 | |
| 53 | −\subsection{Generalized Forecast Error Variance Decomposition} | |
| 45 | +\subsection{Generalized Forecast-Error Variance Decomposition} | |
| 46 | +\label{sec:gfevd} | |
| 54 | 47 | |
| 55 | −Following \citet{DieboldYilmaz2012}, we employ the generalized variance decomposition of \citet{Koop1996} and \citet{Pesaran1998}, which is invariant to the ordering of variables. The $H$-step-ahead generalized forecast error variance decomposition is defined as: | |
| 48 | +Following \citet{DieboldYilmaz2012}, the $H$-step-ahead generalized forecast-error variance decomposition of \citet{Koop1996} and \citet{Pesaran1998} is | |
| 56 | 49 | \begin{equation} |
| 57 | − \theta_{ij}^g(H) = \frac{\sigma_{jj}^{-1} \sum_{h=0}^{H-1} (\mathbf{e}_i' \boldsymbol{\Psi}_h \boldsymbol{\Sigma} \mathbf{e}_j)^2}{\sum_{h=0}^{H-1} \mathbf{e}_i' \boldsymbol{\Psi}_h \boldsymbol{\Sigma} \boldsymbol{\Psi}_h' \mathbf{e}_i}, | |
| 50 | + \theta_{ij}(H) = \frac{\sigma_{jj}^{-1} \sum_{h=0}^{H-1} \left(\mathbf{e}_i' \boldsymbol{\Psi}_h \boldsymbol{\Sigma} \mathbf{e}_j\right)^2}{\sum_{h=0}^{H-1} \mathbf{e}_i' \boldsymbol{\Psi}_h \boldsymbol{\Sigma} \boldsymbol{\Psi}_h' \mathbf{e}_i}, | |
| 58 | 51 | \label{eq:gfevd} |
| 59 | 52 | \end{equation} |
| 60 | −where $\sigma_{jj}$ is the $j$-th diagonal element of $\boldsymbol{\Sigma}$, $\mathbf{e}_i$ is the $i$-th column of $\mathbf{I}_N$, and $H = 10$ days. Since the rows of $\theta_{ij}^g(H)$ do not necessarily sum to unity under the generalized framework, we normalize: | |
| 53 | +where $\sigma_{jj}$ is the $j$-th diagonal element of $\boldsymbol{\Sigma}$ and $\mathbf{e}_i$ is the $i$-th unit vector. The numerator is the contribution of a one-standard-deviation shock to variable $j$---allowing for its contemporaneous correlation with the other shocks---to the $H$-step forecast-error variance of variable $i$, and the denominator is that forecast-error variance. Because the generalized shocks are not orthogonal, the rows of $[\theta_{ij}(H)]$ do not sum to one, and we normalize | |
| 61 | 54 | \begin{equation} |
| 62 | − \tilde{\theta}_{ij}^g(H) = \frac{\theta_{ij}^g(H)}{\sum_{j=1}^{N} \theta_{ij}^g(H)}, | |
| 55 | + \tilde{\theta}_{ij}(H) = \frac{\theta_{ij}(H)}{\sum_{k=1}^{N} \theta_{ik}(H)}, | |
| 56 | + \qquad \sum_{j=1}^{N} \tilde{\theta}_{ij}(H) = 1, | |
| 57 | + \quad \sum_{i,j=1}^{N} \tilde{\theta}_{ij}(H) = N . | |
| 63 | 58 | \label{eq:gfevd_normalized} |
| 64 | 59 | \end{equation} |
| 65 | −such that $\sum_{j=1}^{N} \tilde{\theta}_{ij}^g(H) = 1$ and $\sum_{i,j=1}^{N} \tilde{\theta}_{ij}^g(H) = N$. | |
| 66 | − | |
| 67 | −\subsection{Spillover Measures} | |
| 60 | +We use $H = 10$ trading days, as in \citet{DieboldYilmaz2012}, and report $H \in \{5, 20\}$ as robustness checks. Since the decomposition converges as $H$ grows, the choice of horizon affects the level of the measures more than the ranking of the instruments. | |
| 68 | 61 | |
| 69 | −From the normalized GFEVD matrix $\tilde{\boldsymbol{\Theta}}^g(H) = [\tilde{\theta}_{ij}^g(H)]$, we define four spillover measures. | |
| 62 | +\subsection{Connectedness Measures} | |
| 63 | +\label{sec:measures} | |
| 70 | 64 | |
| 71 | −\paragraph{Total Spillover Index.} | |
| 65 | +All measures are expressed in percent of forecast-error variance. The total spillover index is the share of forecast-error variance in the system that is due to cross-variable shocks, | |
| 72 | 66 | \begin{equation} |
| 73 | − \TSI(H) = \frac{\sum_{\substack{i,j=1 \\ i \neq j}}^{N} \tilde{\theta}_{ij}^g(H)}{N} \times 100. | |
| 67 | + \TSI(H) = \frac{100}{N} \sum_{\substack{i,j=1 \\ i \neq j}}^{N} \tilde{\theta}_{ij}(H) . | |
| 74 | 68 | \label{eq:tsi} |
| 75 | 69 | \end{equation} |
| 76 | − | |
| 77 | −\paragraph{Directional Spillovers TO Others.} The volatility spillover transmitted by market $j$ to all other markets: | |
| 70 | +The directional spillover received by $i$ from all other variables and the spillover transmitted by $j$ to all other variables are the off-diagonal row and column sums, | |
| 78 | 71 | \begin{equation} |
| 79 | − S_{\cdot j}^g(H) = \sum_{\substack{i=1 \\ i \neq j}}^{N} \tilde{\theta}_{ij}^g(H) \times 100. | |
| 80 | − \label{eq:to_spillover} | |
| 72 | + \mathrm{FROM}_i(H) = 100 \sum_{\substack{j=1 \\ j \neq i}}^{N} \tilde{\theta}_{ij}(H), | |
| 73 | + \qquad | |
| 74 | + \mathrm{TO}_j(H) = 100 \sum_{\substack{i=1 \\ i \neq j}}^{N} \tilde{\theta}_{ij}(H), | |
| 75 | + \label{eq:directional} | |
| 81 | 76 | \end{equation} |
| 82 | − | |
| 83 | −\paragraph{Directional Spillovers FROM Others.} The volatility spillover received by market $i$ from all other markets: | |
| 77 | +and the net directional spillover of $i$ is | |
| 84 | 78 | \begin{equation} |
| 85 | − S_{i \cdot}^g(H) = \sum_{\substack{j=1 \\ j \neq i}}^{N} \tilde{\theta}_{ij}^g(H) \times 100. | |
| 86 | − \label{eq:from_spillover} | |
| 79 | + \mathrm{NET}_i(H) = \mathrm{TO}_i(H) - \mathrm{FROM}_i(H) . | |
| 80 | + \label{eq:net_spillover} | |
| 87 | 81 | \end{equation} |
| 88 | − | |
| 89 | −\paragraph{Net Directional Spillovers.} The net volatility spillover for market $i$: | |
| 82 | +$\mathrm{FROM}_i$ lies between 0 and 100; $\mathrm{TO}_j$ is unbounded above and can exceed 100 when a variable explains a large share of many others; and $\mathrm{NET}_i$ is positive for a net transmitter and negative for a net receiver, with $\sum_i \mathrm{NET}_i = 0$. We express $\mathrm{NET}_i$ in percentage points. Finally, the net pairwise directional spillover from $i$ to $j$, | |
| 90 | 83 | \begin{equation} |
| 91 | − S_i^{\text{net}}(H) = S_{\cdot i}^g(H) - S_{i \cdot}^g(H). | |
| 92 | − \label{eq:net_spillover} | |
| 84 | + \mathrm{NET}_{i \to j}(H) = 100\,\big[\tilde{\theta}_{ji}(H) - \tilde{\theta}_{ij}(H)\big], | |
| 85 | + \label{eq:net_pairwise} | |
| 93 | 86 | \end{equation} |
| 94 | −A positive (negative) value indicates that market $i$ is a net transmitter (receiver) of volatility. | |
| 87 | +is the signed edge of the connectedness network of \citet{DieboldYilmaz2014}. | |
| 88 | + | |
| 89 | +\subsection{Inference} | |
| 90 | +\label{sec:inference} | |
| 95 | 91 | |
| 96 | −\subsection{Rolling Window Analysis} | |
| 92 | +The connectedness measures are smooth functions of $(\boldsymbol{\Phi}_1, \ldots, \boldsymbol{\Phi}_p, \boldsymbol{\Sigma})$, and we approximate their sampling distribution with a residual bootstrap \citep{Kilian1998,KilianLutkepohl2017}. Let $\hat{\boldsymbol{\varepsilon}}_t$ denote the centred least-squares residuals of \eqref{eq:var}. For each of $B = 500$ replications, residuals are resampled with replacement, an artificial sample is generated recursively from the estimated coefficients and the first $p$ observed values, the VAR is re-estimated and the measures are recomputed. We report 90\% percentile intervals. The bootstrap treats the residuals as independent and identically distributed and therefore does not capture conditional heteroskedasticity in the innovations of log realized volatility; the intervals should be read as indicative of estimation uncertainty rather than as exact. For the calendar-year sub-samples we use $B = 300$. | |
| 97 | 93 | |
| 98 | −To capture time-varying dynamics, we estimate the VAR model and compute the GFEVD using a rolling window of $w = 200$ trading days, advancing by one day: | |
| 94 | +\subsection{Rolling Windows and Sub-Samples} | |
| 95 | +\label{sec:rolling} | |
| 96 | + | |
| 97 | +Time variation is examined in three complementary ways. First, the VAR and the decomposition are re-estimated over rolling windows of $w$ trading days advancing by one day, | |
| 99 | 98 | \begin{equation} |
| 100 | − \TSI_t(H) = \TSI(H; \mathbf{y}_{t-w+1}, \ldots, \mathbf{y}_t). | |
| 99 | + \TSI_t(H; w) = \TSI\big(H; \mathbf{y}_{t-w+1}, \ldots, \mathbf{y}_t\big), | |
| 101 | 100 | \label{eq:rolling_tsi} |
| 102 | 101 | \end{equation} |
| 102 | +and similarly for $\mathrm{NET}_{i,t}(H; w)$. A ten-variable VAR(4) with intercepts has 41 coefficients per equation, so that a 200-day window leaves fewer than five observations per coefficient; the resulting over-fitting biases the total index upwards and makes it noisy. We therefore report $w \in \{200, 250, 500\}$ and treat the 500-day window as the more reliable description of slow-moving trends. Second, four regime sub-samples are estimated separately with bootstrap intervals: the pre-COVID period (January 2019--February 2020), the COVID crash (March--June 2020), the 2022 rate-hiking cycle (January--December 2022) and the spot-ETF era (11 January 2024--March 2026). For the 85-day COVID window the lag order is reduced to $p = 1$; the VAR(4) estimates on the same window are reported in the appendix for comparison. Third, calendar-year estimates with $p = 2$ track the integration of the cryptocurrencies through the shares of bitcoin's forecast-error variance explained by the traditional instruments and the net pairwise spillovers between bitcoin and ES. | |
| 103 | + | |
| 104 | +\subsection{Granger Causality} | |
| 105 | +\label{sec:granger} | |
| 103 | 106 | |
| 104 | −\subsection{Granger Causality Tests} | |
| 107 | +For a pair of log realized volatilities $(y_{i,t}, y_{j,t})$ we test whether $p$ lags of $y_{j}$ help predict $y_{i}$ beyond $p$ own lags \citep{Granger1969}, with the regression | |
| 108 | +\begin{equation} | |
| 109 | + y_{i,t} = \alpha + \sum_{\ell=1}^{p} \beta_\ell\, y_{i,t-\ell} + \sum_{\ell=1}^{p} \gamma_\ell\, y_{j,t-\ell} + u_t, | |
| 110 | + \qquad H_0 : \gamma_1 = \cdots = \gamma_p = 0 . | |
| 111 | + \label{eq:granger} | |
| 112 | +\end{equation} | |
| 113 | +We report the conventional $F$-statistic, $F = [(\mathrm{RSS}_R - \mathrm{RSS}_U)/p] / [\mathrm{RSS}_U/(T - 2p - 1)]$, and a Wald statistic based on a heteroskedasticity- and autocorrelation-consistent covariance matrix with ten lags \citep{NeweyWest1987}, which is more appropriate for volatility series. Granger causality is a statement about incremental one-day-ahead predictability, not about the economic size of the effect; we therefore also report the sum $\sum_\ell \hat{\gamma}_\ell$, which measures the long-run response of $y_i$ to a unit change in $y_j$ in this bivariate regression. | |
| 114 | + | |
| 115 | +\subsection{Intraday Periodicity and Session-Ordered Predictability} | |
| 116 | +\label{sec:sessions_method} | |
| 117 | + | |
| 118 | +The intraday analysis uses the 5-minute returns directly. Exchange time stamps are converted to Coordinated Universal Time (UTC) with the civil daylight-saving rules of the exchange's time zone, and three sessions are defined in UTC: Asian (00:00--08:00), European (08:00--14:30) and U.S. (14:30--21:00). For each instrument the hourly profile of volatility is the mean absolute 5-minute return by hour of the day, and the session realized variance on day $t$ is | |
| 119 | +\begin{equation} | |
| 120 | + \RV^{s}_{i,t} = \sum_{j \in s} r_{i,t,j}^2, \qquad s \in \{\text{Asian}, \text{European}, \text{U.S.}\}, | |
| 121 | + \label{eq:session_rv} | |
| 122 | +\end{equation} | |
| 123 | +retained when the session contains at least twelve bars. The share of daily variance generated in session $s$ is the average over days of $\RV^{s}_{i,t} / \sum_{s'} \RV^{s'}_{i,t}$. | |
| 105 | 124 | |
| 106 | −For realized volatility series $\RV_{i,t}$ and $\RV_{j,t}$, we test whether lagged values of $\RV_{j,t}$ have predictive power for $\RV_{i,t}$ beyond own lags \citep{Granger1969}. The null hypothesis is tested using an $F$-statistic: | |
| 125 | +The chronological ordering of sessions within a UTC day makes it possible to test whether volatility realized in an earlier session helps predict volatility realized in a later one. We estimate | |
| 107 | 126 | \begin{equation} |
| 108 | − F = \frac{(\text{RSS}_R - \text{RSS}_U) / p}{\text{RSS}_U / (T - 2p - 1)}, | |
| 109 | − \label{eq:granger_f} | |
| 127 | + \ln \RV^{\mathrm{US}}_{i,t} = \alpha + \sum_{\ell=1}^{4} \beta_\ell \ln \RV^{\mathrm{US}}_{i,t-\ell} + \sum_{\ell=0}^{3} \gamma_\ell \ln \RV^{s}_{j,t-\ell} + u_t, | |
| 128 | + \label{eq:session_predictive} | |
| 110 | 129 | \end{equation} |
| 111 | −where $\text{RSS}_R$ and $\text{RSS}_U$ are the residual sums of squares from the restricted and unrestricted models. | |
| 130 | +where $i$ is ES, NQ or the VIX, $j$ is bitcoin and $s$ is the Asian or the European session of the same day, and test $\gamma_0 = \cdots = \gamma_3 = 0$ with a HAC Wald statistic. The reverse direction replaces the dependent variable by bitcoin's Asian-session variance on day $t$ and the predictor by the U.S.-session variance of ES, NQ or the VIX on the previous trading day. A final regression asks whether bitcoin's weekend variance (Saturday plus Sunday) predicts the Monday U.S.-session variance of ES once Friday's ES and bitcoin variances are controlled for. These regressions complement the daily VAR by exploiting an ordering of information that daily data cannot provide. | |
| 112 | 131 | |
| 113 | 132 | \subsection{Network Representation} |
| 133 | +\label{sec:network_method} | |
| 114 | 134 | |
| 115 | −We represent the volatility connectedness structure as a weighted directed graph $\mathcal{G} = (\mathcal{V}, \mathcal{E}, \mathcal{W})$, where the vertex set $\mathcal{V}$ corresponds to the $N$ assets, the edge set $\mathcal{E}$ contains directed edges $(j, i)$ where the GFEVD contribution $\tilde{\theta}_{ij}^g(H)$ exceeds the median of all off-diagonal elements, and edge weight equals the magnitude of the pairwise spillover. Node size is proportional to $S_{\cdot j}^g(H)$, and nodes are colored by asset class. | |
| 135 | +The full-sample decomposition is represented as a directed graph whose nodes are the ten instruments and whose edges are the net pairwise directional spillovers of \eqref{eq:net_pairwise}, drawn from the net transmitter to the net receiver when $|\mathrm{NET}_{i \to j}|$ exceeds the 60th percentile of all pairwise values. Node size is proportional to $\mathrm{TO}_j$ and nodes are coloured by asset class. | |
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| 1 | −% ============================================================================ | |
| 2 | −% REFERENCES | |
| 3 | −% ============================================================================ | |
| 4 | −\newpage | |
| 5 | −\phantomsection | |
| 6 | −\addcontentsline{toc}{section}{References} | |
| 7 | −\bibliographystyle{apalike} | |
| 8 | − | |
| 9 | −\begin{thebibliography}{99} | |
| 10 | − | |
| 11 | −\bibitem[Andersen and Bollerslev(1998)]{Andersen1998} | |
| 12 | −Andersen, T.G. and Bollerslev, T. (1998). | |
| 13 | −Deutsche mark--dollar volatility: Intraday activity patterns, macroeconomic announcements, and longer-run dependencies. | |
| 14 | −\textit{The Journal of Finance}, 53(1):219--265. | |
| 15 | − | |
| 16 | −\bibitem[Andersen et~al.(2001)]{Andersen2001} | |
| 17 | −Andersen, T.G., Bollerslev, T., Diebold, F.X., and Labys, P. (2001). | |
| 18 | −The distribution of realized exchange rate volatility. | |
| 19 | −\textit{Journal of the American Statistical Association}, 96(453):42--55. | |
| 20 | − | |
| 21 | −\bibitem[Andersen et~al.(2003)]{Andersen2003} | |
| 22 | −Andersen, T.G., Bollerslev, T., Diebold, F.X., and Labys, P. (2003). | |
| 23 | −Modeling and forecasting realized volatility. | |
| 24 | −\textit{Econometrica}, 71(2):579--625. | |
| 25 | − | |
| 26 | −\bibitem[Ang and Bekaert(2002)]{Ang2002} | |
| 27 | −Ang, A. and Bekaert, G. (2002). | |
| 28 | −International asset allocation with regime shifts. | |
| 29 | −\textit{Review of Financial Studies}, 15(4):1137--1187. | |
| 30 | − | |
| 31 | −\bibitem[Ante(2021)]{Ante2021} | |
| 32 | −Ante, L. (2021). | |
| 33 | −How Elon Musk's Twitter activity moves cryptocurrency markets. | |
| 34 | −\textit{Technological Forecasting and Social Change}, 186:122112. | |
| 35 | − | |
| 36 | −\bibitem[Antonakakis et~al.(2020)]{Antonakakis2020} | |
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| 39 | −\textit{Journal of Risk and Financial Management}, 13(4):84. | |
| 40 | − | |
| 41 | −\bibitem[Baele(2005)]{Baele2005} | |
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| 44 | −\textit{Journal of Financial and Quantitative Analysis}, 40(2):373--401. | |
| 45 | − | |
| 46 | −\bibitem[Barndorff-Nielsen and Shephard(2002)]{BarndorffNielsen2002} | |
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| 48 | −Econometric analysis of realized volatility and its use in estimating stochastic volatility models. | |
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| 50 | − | |
| 51 | −\bibitem[Barunik et~al.(2016)]{Barunik2016} | |
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| 54 | −\textit{Journal of Financial Markets}, 27:55--78. | |
| 55 | − | |
| 56 | −\bibitem[Barunik and Krehlik(2018)]{Barunik2018} | |
| 57 | −Barunik, J. and Krehlik, T. (2018). | |
| 58 | −Measuring the frequency dynamics of financial connectedness and systemic risk. | |
| 59 | −\textit{Journal of Financial Econometrics}, 16(2):271--296. | |
| 60 | − | |
| 61 | −\bibitem[Baur and Lucey(2010)]{Baur2010} | |
| 62 | −Baur, D.G. and Lucey, B.M. (2010). | |
| 63 | −Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. | |
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| 65 | − | |
| 66 | −\bibitem[Bouri et~al.(2017)]{Bouri2017} | |
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| 70 | − | |
| 71 | −\bibitem[Bouri et~al.(2019)]{Bouri2019} | |
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| 74 | −\textit{The Quarterly Review of Economics and Finance}, 77:156--164. | |
| 75 | − | |
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modified
paper/sections/results.tex
+147 −183
@@ -3,299 +3,263 @@ | ||
| 3 | 3 | \label{sec:results} |
| 4 | 4 | % ============================================================================ |
| 5 | 5 | |
| 6 | −\subsection{Full-Sample Connectedness Analysis} | |
| 6 | +\subsection{Full-Sample Connectedness} | |
| 7 | +\label{sec:full_sample} | |
| 7 | 8 | |
| 8 | −\Cref{tab:connectedness_full} presents the full-sample Diebold--Yilmaz connectedness table based on a VAR(4) model with generalized variance decomposition at a 10-day forecast horizon. The sample encompasses the common period across all 10 assets (2016--2026). | |
| 9 | +\Cref{tab:connectedness_full} reports the full-sample connectedness table for log realized volatility over the 2{,}514 trading days from March 2016 to March 2026, with a VAR(4) and $H = 10$. Entry $(i, j)$ is the percentage of the ten-day forecast-error variance of instrument $i$ attributable to shocks in instrument $j$; the last column and the last two rows give the FROM, TO and NET measures of \eqref{eq:directional}--\eqref{eq:net_spillover}, each followed by its 90\% bootstrap interval. | |
| 9 | 10 | |
| 10 | 11 | \begin{table}[htbp] |
| 11 | 12 | \centering |
| 12 | −\caption{Full-Sample Diebold--Yilmaz Connectedness Table.} | |
| 13 | +\caption{Full-sample connectedness table, log realized volatility, VAR(4), $H = 10$.} | |
| 13 | 14 | \label{tab:connectedness_full} |
| 15 | +\adjustbox{max width=\textwidth, max totalheight=0.80\textheight}{% | |
| 14 | 16 | \begin{threeparttable} |
| 15 | −\begin{adjustbox}{max width=\textwidth} | |
| 16 | −\begin{tabular}{@{}l*{10}{r}r@{}} | |
| 17 | −\toprule | |
| 18 | −& \multicolumn{10}{c}{FROM (shock origin)} & \\ | |
| 19 | −\cmidrule(lr){2-11} | |
| 20 | −TO & ES & NQ & EURUSD & USDJPY & GBPUSD & GC & CL & BTC & ETH & VIX & FROM \\ | |
| 21 | −\midrule | |
| 22 | −ES & 28.6 & 25.5 & 8.4 & 6.6 & 7.1 & 9.1 & 8.4 & 0.2 & 0.2 & 5.9 & 71.4 \\ | |
| 23 | −NQ & 26.7 & 27.6 & 8.7 & 6.5 & 7.4 & 9.0 & 8.1 & 0.2 & 0.2 & 5.5 & 72.4 \\ | |
| 24 | −EURUSD & 11.4 & 11.2 & 25.7 & 14.3 & 17.4 & 11.0 & 8.0 & 0.0 & 0.2 & 0.7 & 74.3 \\ | |
| 25 | −USDJPY & 8.9 & 8.7 & 15.7 & 38.6 & 11.6 & 9.1 & 5.6 & 0.1 & 0.3 & 1.5 & 61.4 \\ | |
| 26 | −GBPUSD & 11.1 & 10.6 & 18.7 & 11.7 & 29.6 & 9.8 & 7.7 & 0.1 & 0.2 & 0.5 & 70.4 \\ | |
| 27 | −GC & 11.8 & 11.4 & 12.7 & 9.5 & 9.6 & 34.5 & 8.0 & 0.2 & 0.2 & 2.1 & 65.5 \\ | |
| 28 | −CL & 12.9 & 11.2 & 7.9 & 5.0 & 7.1 & 9.3 & 45.3 & 0.0 & 0.1 & 1.2 & 54.7 \\ | |
| 29 | −BTC & 0.1 & 0.1 & 0.1 & 0.2 & 0.1 & 0.3 & 0.1 & 79.3 & 19.3 & 0.4 & 20.7 \\ | |
| 30 | −ETH & 0.2 & 0.3 & 0.2 & 0.3 & 0.1 & 0.2 & 0.2 & 20.6 & 77.9 & 0.1 & 22.1 \\ | |
| 31 | −VIX & 15.0 & 13.2 & 2.2 & 2.5 & 1.4 & 4.8 & 1.4 & 0.4 & 0.4 & 58.6 & 41.4 \\ | |
| 32 | −\midrule | |
| 33 | −TO & 98.2 & 92.2 & 74.7 & 56.4 & 61.8 & 62.6 & 47.6 & 21.9 & 21.1 & 18.0 & \textbf{55.4} \\ | |
| 34 | −NET & $+$26.8 & $+$19.7 & $+$0.4 & $-$5.0 & $-$8.7 & $-$2.9 & $-$7.2 & $+$1.2 & $-$1.0 & $-$23.4 & \\ | |
| 35 | −\bottomrule | |
| 36 | −\end{tabular} | |
| 37 | −\end{adjustbox} | |
| 17 | +\input{tables/tab_connectedness_full} | |
| 38 | 18 | \begin{tablenotes}[flushleft] |
| 39 | 19 | \footnotesize |
| 40 | −\item \textit{Notes:} Generalized forecast error variance decomposition from a VAR(4) model at horizon $H=10$. Entry $(i,j)$ is the percentage of the 10-day-ahead forecast error variance of asset $i$ attributable to shocks in asset $j$. FROM = total spillover received. TO = total spillover transmitted. NET = TO $-$ FROM. The lower-right entry (55.4) is the Total Spillover Index. | |
| 20 | +\item \textit{Notes:} Generalized forecast-error variance decomposition, 2016-03-11 to 2026-03-11, $T = 2{,}514$ trading days. Entry $(i,j)$ is the share (\%) of the 10-day-ahead forecast-error variance of the log realized volatility of $i$ due to shocks in $j$; diagonal entries (own shares) in bold. FROM and TO are the off-diagonal row and column sums; NET $=$ TO $-$ FROM in percentage points; the bottom-right entry of the TO row is the total spillover index. Figures in brackets are 90\% percentile intervals from a residual bootstrap with 500 replications. Source: \path{results/rev_table_connectedness_full.csv} and \path{rev_table_connectedness_full_ci.csv}. | |
| 41 | 21 | \end{tablenotes} |
| 42 | −\end{threeparttable} | |
| 22 | +\end{threeparttable}} | |
| 43 | 23 | \end{table} |
| 44 | 24 | |
| 45 | −The total spillover index is 55.44\%, indicating that more than half of all forecast error variance in the system is attributable to cross-asset shocks rather than own-asset dynamics. Several key findings emerge: | |
| 25 | +The total spillover index is 54.8\%, with a 90\% interval of 53.1--56.9\%: slightly more than half of the forecast-error variance of the system is attributable to cross-asset shocks. Four features of the table organize the discussion. | |
| 46 | 26 | |
| 47 | −\textit{Equity futures dominate volatility transmission.} ES and NQ are the largest net volatility transmitters, with net directional spillovers of $+26.80\%$ and $+19.72\%$, respectively. Together, they transmit a combined 190.4\% of directional spillovers to other markets, reflecting the central role of U.S.\ equity markets in global price discovery. | |
| 27 | +First, equity index futures are the dominant transmitters. ES and NQ transmit 104\% and 92\% of forecast-error variance to the other nine series and receive 68\% and 66\%, for net spillovers of $+36.0$ (interval 29.9--41.5) and $+25.6$ (19.0--31.3) percentage points. Shocks to ES explain 12\% of the variance of crude oil, 11\% of gold, 8--9\% of each exchange rate and 21\% of the realized volatility of the VIX; conversely, no other series explains more than 12\% of ES. The two contracts are also each other's largest source of variance (28--30\%), as expected for two indices of the same market. | |
| 48 | 28 | |
| 49 | −\textit{VIX is a net receiver, not a transmitter.} Despite its role as the ``fear gauge,'' VIX is the largest net receiver of volatility shocks ($-23.37\%$). Its forecast error variance is explained primarily by ES (15.0\%) and NQ (13.2\%) shocks, consistent with VIX being derived from S\&P 500 options. | |
| 29 | +Second, the realized volatility of the VIX is the largest net receiver, at $-20.6$ percentage points (interval $-25.2$ to $-14.0$). Shocks to ES and NQ explain 21.2\% and 18.5\% of its forecast-error variance, while its own shocks explain only 40\%; it transmits 40\% in total, of which 12\% and 11\% to ES and NQ. This is the pattern one expects for a price that is a deterministic function of S\&P~500 option prices and whose intraday variability therefore inherits that of the underlying. It is not a statement about the information content of the VIX level for future volatility, which is a separate question \citep{BekaertHoerova2014}. Crude oil ($-14.2$, interval $-21.6$ to $-6.7$) and sterling ($-13.2$, interval $-18.0$ to $-7.4$) are the other clear net receivers; gold ($-7.2$) and USD/JPY ($-5.2$) are mild receivers whose intervals touch or include zero, and EUR/USD is neutral. | |
| 50 | 30 | |
| 51 | −\textit{Crypto markets form an isolated cluster.} BTC and ETH exhibit remarkably high own-shock contributions (79.3\% and 77.9\%) and negligible cross-asset spillovers ($<0.5\%$). The pairwise BTC--ETH spillover is substantial ($\approx$20\%), but connections to traditional assets are minimal. | |
| 31 | +Third, bitcoin and ether form a distinct block. Each explains 27--28\% of the other's variance, and their own shares, at 67\% and 65\%, are the largest in the table. Their exposure to the eight traditional instruments is small but not negligible in the full sample: 6.3\% of bitcoin's and 7.1\% of ether's forecast-error variance, of which ES and NQ account for about half. Their net spillovers, $+1.7$ (interval $-3.3$ to $6.4$) for bitcoin and $-2.4$ ($-7.9$ to $2.1$) for ether, are not distinguishable from zero. The earlier version of this paper reported own shares above 77\% and cross-asset shares below 0.5\% for the cryptocurrencies; those figures were produced by a panel in which the traditional series were forward-filled on weekends, which mechanically breaks the contemporaneous correlation between crypto innovations and the (artificially zero) innovations of the other series. | |
| 52 | 32 | |
| 53 | −\textit{FX and commodity markets show moderate interconnectedness.} EURUSD receives significant spillovers from GBPUSD (17.4\%) and USDJPY (14.3\%), reflecting the common U.S.\ dollar factor. CL is the most self-dependent among traditional assets (45.3\% own contribution). | |
| 33 | +Fourth, the exchange rates and commodities form a middle tier. EUR/USD receives 16.5\% of its variance from GBP/USD and 14.4\% from USD/JPY, GBP/USD receives 19.3\% from EUR/USD, and gold receives about 10\% each from the two European currencies, which is consistent with a common dollar factor in all these prices. Crude oil has the largest own share among traditional assets (54\%), receives most of its cross-asset variance from ES and NQ (22\% together) and transmits little, which is at odds with a view of oil as an originator of macroeconomic volatility over this decade. | |
| 54 | 34 | |
| 55 | −\Cref{fig:connectedness_heatmap} provides a visual representation of the connectedness matrix. | |
| 35 | +\Cref{fig:connectedness_heatmap} displays the matrix graphically. The block structure is visible: a dense equity--FX--commodity core, a two-node crypto block linked to the core mainly through the equity futures, and the VIX attached to the core almost exclusively through ES and NQ. | |
| 56 | 36 | |
| 57 | 37 | \begin{figure}[htbp] |
| 58 | 38 | \centering |
| 59 | 39 | \includegraphics[width=0.85\textwidth]{fig2_connectedness_heatmap.png} |
| 60 | −\caption{Diebold--Yilmaz Connectedness Heatmap (Full Sample).} | |
| 40 | +\caption{Full-sample variance-decomposition shares.} | |
| 61 | 41 | \label{fig:connectedness_heatmap} |
| 62 | 42 | \begin{minipage}{0.95\textwidth} |
| 63 | 43 | \vspace{4pt} |
| 64 | −\footnotesize\textit{Notes:} Color intensity represents the magnitude of pairwise forecast error variance contributions. Three distinct clusters emerge: (i)~a tightly connected equity--FX--commodity block; (ii)~an isolated crypto cluster (BTC--ETH); and (iii)~VIX as a peripheral receiver connected primarily to equities. | |
| 44 | +\footnotesize\textit{Notes:} Shares (\%) of the 10-day forecast-error variance of the row instrument attributable to shocks in the column instrument, from \Cref{tab:connectedness_full}. Darker cells denote larger shares. | |
| 65 | 45 | \end{minipage} |
| 66 | 46 | \end{figure} |
| 67 | 47 | |
| 48 | +\subsection{Robustness of the Full-Sample Results} | |
| 49 | +\label{sec:robustness} | |
| 50 | + | |
| 51 | +\Cref{tab:robustness} re-estimates the full-sample decomposition under alternative choices. The total index lies between 53.7\% and 55.5\% for $p \in \{1, 2, 3, 4, 6\}$ and between 54.4\% and 55.3\% for $H \in \{5, 10, 20\}$; it falls to 50.0\% when realized volatility enters in levels rather than logarithms, because the covariance matrix is then dominated by a few extreme days on which comovement is weaker than on ordinary days. Including weekend crypto variance in the Monday observation leaves every measure within one percentage point of the baseline. Excluding the two cryptocurrencies raises the index to 59.0\%, which quantifies the dilution they induce, and excluding the VIX lowers it to 52.9\%. | |
| 52 | + | |
| 53 | +\begin{table}[htbp] | |
| 54 | +\centering | |
| 55 | +\caption{Robustness of full-sample connectedness to specification and sample choices.} | |
| 56 | +\label{tab:robustness} | |
| 57 | +\adjustbox{max width=\textwidth}{% | |
| 58 | +\begin{threeparttable} | |
| 59 | +\input{tables/tab_robustness} | |
| 60 | +\begin{tablenotes}[flushleft] | |
| 61 | +\footnotesize | |
| 62 | +\item \textit{Notes:} TSI in percent; ES, NQ, USDJPY, CL, BTC and VIX columns are net directional spillovers in percentage points; the last column is bitcoin's own variance share (\%). Baseline: log realized volatility, trading-day panel, VAR(4), $H = 10$. ``Weekend-inclusive crypto RV'' averages the daily variance of BTC and ETH over the calendar days since the previous trading day. Source: \path{results/rev_table_robustness.csv}. | |
| 63 | +\end{tablenotes} | |
| 64 | +\end{threeparttable}} | |
| 65 | +\end{table} | |
| 66 | + | |
| 67 | +The ranking of the main transmitters and receivers is stable: ES is the largest net transmitter in every row of the table (between $+26$ and $+42$ percentage points), NQ the second, and the realized volatility of the VIX the largest net receiver (between $-17$ and $-27$), followed by crude oil (between $-6$ and $-17$). The net position of bitcoin, by contrast, is not robust in sign: it is $+7.4$ with one lag, $+4.4$ at $H = 20$, $-0.3$ at $H = 5$, $-1.3$ when ether is excluded, $+3.0$ in 2016--2019 and $-8.7$ in 2020--2026. Bitcoin's own share falls from 78\% in 2016--2019 to 48\% in 2020--2026, the clearest sign in the table that its integration with the system increased. The sub-sample split also reverses the sign of USD/JPY, a net transmitter before 2020 ($+9.9$) and a net receiver after ($-11.3$), and raises the total index from 51.5\% to 60.9\%. | |
| 68 | + | |
| 68 | 69 | \subsection{Time-Varying Connectedness} |
| 70 | +\label{sec:rolling_results} | |
| 69 | 71 | |
| 70 | −\Cref{fig:rolling_spillover} presents the rolling 200-day total spillover index over the 2016--2026 period. | |
| 72 | +\Cref{fig:rolling_spillover} plots the rolling total spillover index for windows of 200, 250 and 500 trading days. The three series tell the same story at different levels of smoothing. Connectedness was moderate and declining from 2016 to late 2017, reaching its minimum of 50.5\% (200-day window) in October 2017, when the cryptocurrency boom decoupled bitcoin and ether from everything else. It then fluctuated between 51\% and 61\% until February 2020 and rose sharply during the COVID-19 crash: the 200-day index moved from 60.4\% on 20 February 2020 to 69.1\% on 31 March 2020 and remained above 65\% until the end of June. The 2021 decline, the renewed increase through the 2022 tightening cycle (the 200-day index exceeds 70\% in September--October 2022), the trough of early 2024 and the climb through 2025 are all visible in the 500-day window, which ends the sample at its own maximum of 66.5\% in March 2026. The 200-day index reaches the highest value of the entire sample, 73.4\%, on 24 September 2025; the calendar-year estimates of \Cref{sec:yearly} confirm that 2025 is the most connected year of the decade, at 71.5\% (interval 67.9--75.2). | |
| 71 | 73 | |
| 72 | 74 | \begin{figure}[htbp] |
| 73 | 75 | \centering |
| 74 | 76 | \includegraphics[width=\textwidth]{fig3_rolling_spillover.png} |
| 75 | −\caption{Rolling 200-Day Total Spillover Index with Event Markers.} | |
| 77 | +\caption{Rolling total spillover index.} | |
| 76 | 78 | \label{fig:rolling_spillover} |
| 77 | 79 | \begin{minipage}{0.95\textwidth} |
| 78 | 80 | \vspace{4pt} |
| 79 | −\footnotesize\textit{Notes:} Total spillover index from a VAR(4) model with generalized variance decomposition at $H=10$, estimated over rolling 200-day windows. Dashed horizontal line: full-period mean (67.13\%). Vertical lines mark: COVID-19 crash (March 2020), Federal Reserve rate hikes (March 2022), crypto winter (June 2022), FTX collapse (November 2022). | |
| 81 | +\footnotesize\textit{Notes:} Total spillover index (\%) from a VAR(4) on log realized volatility with $H = 10$, estimated over rolling windows of 200, 250 and 500 trading days and plotted at the last day of the window. The dashed line is the full-sample estimate (54.8\%). Vertical lines mark the COVID-19 crash (16 March 2020), the first Federal Reserve rate increase of the 2022 cycle (16 March 2022), the FTX collapse (11 November 2022), the launch of spot bitcoin ETFs (11 January 2024) and the volatility spike of 5 August 2024. Source: \path{results/rev_rolling_w200.csv}, \path{rev_rolling_w250.csv}, \path{rev_rolling_w500.csv}. | |
| 80 | 82 | \end{minipage} |
| 81 | 83 | \end{figure} |
| 82 | 84 | |
| 83 | −The rolling total spillover index exhibits substantial time variation, ranging from 57.22\% to 81.55\% (mean: 67.13\%). Several episodes are noteworthy: | |
| 84 | − | |
| 85 | −\begin{enumerate}[label=(\roman*)] | |
| 86 | − \item \textbf{February 2018 (TSI = 81.55\%):} The maximum coincides with the ``Volmageddon'' event, when short-volatility ETPs imploded, triggering cascading volatility across all asset classes. | |
| 87 | − \item \textbf{COVID-19 crash (March 2020):} The TSI initially dips during the acute phase before rising sharply, reflecting initial de-correlation followed by re-coupling through coordinated monetary policy responses. | |
| 88 | − \item \textbf{2022 rate-hiking cycle:} The TSI rises steadily to 72--75\%, reflecting the macro-driven nature of the volatility environment. | |
| 89 | − \item \textbf{Post-FTX collapse (November 2022):} The TSI shows a temporary decline, consistent with the crypto winter being contained within the crypto ecosystem. | |
| 90 | − \item \textbf{2024--2025 elevation:} The TSI trends upward, potentially reflecting growing crypto integration through spot Bitcoin ETF approvals and institutional participation. | |
| 91 | −\end{enumerate} | |
| 85 | +Two differences from the May 2026 version deserve mention. First, the level of the rolling index is lower (mean 61.9\% for 200 trading days against 67.1\% previously) and the 500-day mean of 58.3\% is closer to the full-sample value of 54.8\%; the gap between rolling and full-sample estimates is the small-sample upward bias of a heavily parameterized VAR, which shrinks as the window lengthens (\Cref{tab:rolling_summary} in the appendix). Second, the earlier version reported a maximum of 81.6\% on 6 February 2018, interpreted as the signature of the ``Volmageddon'' episode, with the index jumping from 62\% to 82\% in two days. On the trading-day panel the index moves from 54.4\% on 2 February to 56.4\% on 6 February 2018. The earlier spike was produced by the interaction of a single extreme observation of VIX realized volatility with a panel in which most other series were forward-filled on surrounding weekend days; it is not a feature of the data. | |
| 92 | 86 | |
| 93 | 87 | \subsection{Regime-Specific Connectedness} |
| 88 | +\label{sec:regimes} | |
| 94 | 89 | |
| 95 | −We estimate separate connectedness tables for three distinct regimes: pre-COVID (January 2019--February 2020), COVID crash (March--June 2020), and 2022 rate-hiking cycle (January--December 2022). | |
| 96 | − | |
| 97 | −\subsubsection{Pre-COVID Regime (January 2019--February 2020)} | |
| 90 | +\Cref{tab:regimes} summarizes the decomposition in four sub-samples, with bootstrap intervals; the full ten-by-ten tables are in \Cref{sec:appendix_regimes}, and \Cref{fig:net_spillovers_regimes} plots the net spillovers. | |
| 98 | 91 | |
| 99 | 92 | \begin{table}[htbp] |
| 100 | 93 | \centering |
| 101 | −\caption{Connectedness Table --- Pre-COVID Regime (2019-01 to 2020-02).} | |
| 102 | −\label{tab:connectedness_precovid} | |
| 94 | +\caption{Total and net directional spillovers by regime, with 90\% bootstrap intervals.} | |
| 95 | +\label{tab:regimes} | |
| 103 | 96 | \begin{threeparttable} |
| 104 | −\begin{adjustbox}{max width=\textwidth} | |
| 105 | −\begin{tabular}{@{}l*{10}{r}r@{}} | |
| 106 | −\toprule | |
| 107 | −& ES & NQ & EURUSD & USDJPY & GBPUSD & GC & CL & BTC & ETH & VIX & FROM \\ | |
| 108 | −\midrule | |
| 109 | −ES & 31.3 & 29.0 & 4.1 & 9.4 & 1.6 & 8.5 & 6.5 & 0.0 & 0.7 & 8.9 & 68.7 \\ | |
| 110 | −NQ & 30.5 & 29.2 & 4.2 & 9.8 & 1.7 & 8.5 & 6.8 & 0.1 & 0.7 & 8.6 & 70.8 \\ | |
| 111 | −EURUSD & 12.8 & 13.1 & 24.1 & 12.9 & 13.6 & 12.3 & 9.5 & 0.2 & 0.3 & 1.4 & 75.9 \\ | |
| 112 | −USDJPY & 21.6 & 20.8 & 7.1 & 20.5 & 3.2 & 11.9 & 7.5 & 0.1 & 0.3 & 7.2 & 79.5 \\ | |
| 113 | −GBPUSD & 8.6 & 8.4 & 18.0 & 7.8 & 37.5 & 8.8 & 7.8 & 0.4 & 0.8 & 2.0 & 62.5 \\ | |
| 114 | −GC & 15.9 & 16.2 & 9.1 & 14.7 & 4.6 & 25.0 & 9.4 & 0.7 & 0.2 & 4.3 & 75.0 \\ | |
| 115 | −CL & 17.1 & 17.9 & 7.4 & 12.9 & 5.1 & 11.0 & 25.7 & 0.2 & 0.2 & 2.5 & 74.3 \\ | |
| 116 | −BTC & 7.1 & 5.6 & 0.2 & 1.4 & 0.3 & 2.2 & 1.7 & 73.0 & 6.8 & 1.7 & 27.0 \\ | |
| 117 | −ETH & 6.7 & 6.0 & 0.6 & 1.4 & 0.4 & 1.7 & 2.4 & 24.6 & 55.2 & 1.0 & 44.8 \\ | |
| 118 | −VIX & 24.9 & 22.9 & 1.8 & 8.0 & 0.3 & 5.5 & 3.3 & 0.9 & 1.2 & 31.4 & 68.6 \\ | |
| 119 | −\midrule | |
| 120 | −TO & 145.2 & 139.7 & 52.6 & 78.1 & 30.6 & 70.4 & 54.8 & 27.0 & 11.1 & 37.7 & \textbf{64.7} \\ | |
| 121 | −NET & $+$76.4 & $+$68.9 & $-$23.3 & $-$1.4 & $-$31.8 & $-$4.6 & $-$19.6 & $-$0.0 & $-$33.7 & $-$30.9 & \\ | |
| 122 | −\bottomrule | |
| 123 | −\end{tabular} | |
| 124 | −\end{adjustbox} | |
| 97 | +\small | |
| 98 | +\input{tables/tab_regimes} | |
| 125 | 99 | \begin{tablenotes}[flushleft] |
| 126 | 100 | \footnotesize |
| 127 | −\item \textit{Notes:} Same methodology as \Cref{tab:connectedness_full}. TSI = 64.72\%. | |
| 101 | +\item \textit{Notes:} Log realized volatility, $H = 10$; $p = 4$ except for the 85-day COVID window, where $p = 1$ (the VAR(4) estimates for that window are TSI 71.4\%, NET USDJPY $+105.3$, NET BTC $-4.6$). Brackets: 90\% percentile intervals from 500 residual-bootstrap replications. The spot-ETF era begins on 11 January 2024, the first trading day of U.S. spot bitcoin ETFs. Source: \path{results/rev_table_regimes.csv}. | |
| 128 | 102 | \end{tablenotes} |
| 129 | 103 | \end{threeparttable} |
| 130 | 104 | \end{table} |
| 131 | 105 | |
| 132 | −During the pre-COVID regime, the volatility hierarchy is dominated overwhelmingly by U.S.\ equity futures. ES and NQ exhibit net spillovers of $+76.4\%$ and $+68.9\%$---far exceeding their full-sample values. | |
| 106 | +\begin{figure}[htbp] | |
| 107 | +\centering | |
| 108 | +\includegraphics[width=\textwidth]{fig4_net_spillovers_regimes.png} | |
| 109 | +\caption{Net directional spillovers by regime.} | |
| 110 | +\label{fig:net_spillovers_regimes} | |
| 111 | +\begin{minipage}{0.95\textwidth} | |
| 112 | +\vspace{4pt} | |
| 113 | +\footnotesize\textit{Notes:} Net directional spillovers (percentage points) from \Cref{tab:regimes}; whiskers are 90\% bootstrap intervals. Positive values denote net transmitters. | |
| 114 | +\end{minipage} | |
| 115 | +\end{figure} | |
| 133 | 116 | |
| 134 | −\subsubsection{COVID Crash Regime (March--June 2020)} | |
| 117 | +In the pre-COVID period (292 days) the equity futures dominate even more than in the full sample, with net spillovers of $+41$ and $+47$ percentage points and intervals that exclude zero by a wide margin; the European currencies and crude oil are significant net receivers; and the VIX is neutral. Bitcoin's point estimate is $+12.7$, but its interval ($-14.8$ to $+24.0$) spans zero. | |
| 135 | 118 | |
| 136 | −\begin{table}[htbp] | |
| 137 | −\centering | |
| 138 | −\caption{Connectedness Table --- COVID Crash Regime (2020-03 to 2020-06).} | |
| 139 | −\label{tab:connectedness_covid} | |
| 140 | −\begin{threeparttable} | |
| 141 | −\begin{adjustbox}{max width=\textwidth} | |
| 142 | −\begin{tabular}{@{}l*{10}{r}r@{}} | |
| 143 | −\toprule | |
| 144 | −& ES & NQ & EURUSD & USDJPY & GBPUSD & GC & CL & BTC & ETH & VIX & FROM \\ | |
| 145 | −\midrule | |
| 146 | −ES & 20.1 & 20.6 & 10.9 & 16.2 & 9.6 & 7.2 & 5.6 & 4.4 & 2.4 & 3.1 & 79.9 \\ | |
| 147 | −NQ & 19.4 & 21.1 & 10.8 & 16.7 & 9.4 & 7.3 & 5.8 & 3.9 & 2.2 & 3.3 & 78.9 \\ | |
| 148 | −EURUSD & 8.5 & 9.7 & 21.8 & 19.9 & 17.8 & 10.2 & 7.6 & 1.0 & 1.5 & 2.1 & 78.2 \\ | |
| 149 | −USDJPY & 5.6 & 7.9 & 14.4 & 33.6 & 11.1 & 7.3 & 3.9 & 5.4 & 3.0 & 8.0 & 66.4 \\ | |
| 150 | −GBPUSD & 11.1 & 11.3 & 17.0 & 18.6 & 23.9 & 7.9 & 5.4 & 2.1 & 2.0 & 0.6 & 76.1 \\ | |
| 151 | −GC & 8.1 & 9.6 & 13.0 & 14.4 & 9.2 & 23.6 & 12.4 & 3.9 & 4.3 & 1.6 & 76.4 \\ | |
| 152 | −CL & 4.6 & 5.2 & 8.7 & 4.5 & 6.5 & 17.2 & 49.0 & 1.5 & 2.2 & 0.6 & 51.0 \\ | |
| 153 | −BTC & 2.6 & 2.8 & 5.9 & 16.2 & 2.2 & 6.3 & 6.5 & 34.8 & 16.0 & 6.9 & 65.2 \\ | |
| 154 | −ETH & 3.4 & 3.2 & 4.0 & 8.2 & 1.1 & 3.1 & 4.4 & 17.3 & 51.6 & 3.8 & 48.4 \\ | |
| 155 | −VIX & 5.5 & 7.2 & 7.6 & 12.0 & 5.6 & 0.7 & 0.7 & 4.3 & 2.5 & 54.0 & 46.0 \\ | |
| 156 | −\midrule | |
| 157 | −TO & 68.7 & 77.3 & 92.2 & 126.7 & 72.3 & 67.2 & 52.1 & 43.9 & 36.2 & 30.0 & \textbf{66.7} \\ | |
| 158 | −NET & $-$11.2 & $-$1.6 & $+$14.0 & $+$60.3 & $-$3.7 & $-$9.2 & $+$1.1 & $-$21.3 & $-$12.3 & $-$16.1 & \\ | |
| 159 | −\bottomrule | |
| 160 | −\end{tabular} | |
| 161 | −\end{adjustbox} | |
| 162 | −\begin{tablenotes}[flushleft] | |
| 163 | −\footnotesize | |
| 164 | −\item \textit{Notes:} Same methodology as \Cref{tab:connectedness_full}. TSI = 66.66\%. | |
| 165 | −\end{tablenotes} | |
| 166 | −\end{threeparttable} | |
| 167 | −\end{table} | |
| 119 | +The COVID crash window (85 trading days) is the sub-sample in which inference matters most. The total index rises to 71.7\% (interval 65.9--78.1), the highest of the four regimes. USD/JPY becomes the dominant transmitter, at $+81.8$ percentage points with an interval of $+7.3$ to $+135.3$: the sign is established, the magnitude is not. The economic reading is that the yen's safe-haven appreciation and the unwinding of carry trades in March 2020 \citep{Ranaldo2010,Habib2012}, together with the dollar funding squeeze, made exchange-rate volatility the common factor of that episode. ES and NQ remain net transmitters in point estimate ($+19$ and $+33$) but with intervals that include zero, which corrects the earlier version's statement that equities ``flipped'' to receivers; that statement rested on a VAR(4) with 41 coefficients per equation estimated on 122 calendar days. Bitcoin is a net receiver in point estimate ($-14.4$), consistent with \citet{ConlonMcGee2020}, but its interval is $-45.9$ to $+32.9$. The only other significant result of the window is that the realized volatility of the VIX is a strong net receiver ($-46.6$, interval $-61.4$ to $-11.2$). | |
| 120 | + | |
| 121 | +In the 2022 tightening cycle (254 days) the hierarchy is flatter. ES remains a significant transmitter ($+25.4$) but NQ is neutral; USD/JPY ($-18.6$) and crude oil ($-21.6$) are significant receivers; the European currencies and gold have positive but insignificant point estimates. Bitcoin's net spillover is $-3.4$ with an interval of $-16.7$ to $+12.4$. The earlier version reported $+7.9$ for bitcoin in this regime and described a transition to net transmitter; on the trading-day panel with log volatility the point estimate is negative and, more importantly, the interval shows that the data cannot distinguish either sign from zero in a one-year window. | |
| 168 | 122 | |
| 169 | −The COVID crash regime reveals a dramatic restructuring of the volatility hierarchy. USDJPY emerges as the dominant volatility transmitter ($+60.29\%$ net), reflecting massive safe-haven demand for the Japanese yen. ES flips from its usual transmitter role to a net receiver ($-11.2\%$), and BTC becomes a substantial net receiver ($-21.3\%$), contradicting the narrative of Bitcoin as a safe-haven asset. | |
| 123 | +The spot-ETF era (544 days) is the regime with the sharpest crypto results. The equity futures are back at the top ($+29.4$ and $+28.7$, both significant), crude oil remains a significant receiver ($-19.9$), and bitcoin and ether are both significant net receivers, at $-12.4$ (interval $-20.4$ to $-2.1$) and $-19.5$ ($-27.7$ to $-9.2$). As cryptocurrencies became accessible through regulated equity-market vehicles, their realized volatility became more responsive to shocks in the traditional system without the reverse becoming true. | |
| 170 | 124 | |
| 171 | −\subsubsection{Rate-Hiking Regime (January--December 2022)} | |
| 125 | +\subsection{Crypto Integration by Calendar Year} | |
| 126 | +\label{sec:yearly} | |
| 127 | + | |
| 128 | +\Cref{tab:yearly} and \Cref{fig:yearly_integration} follow the integration of the cryptocurrencies year by year. The share of bitcoin's forecast-error variance explained by the eight traditional instruments (that is, FROM excluding ether) was 13.8\% in 2016, 8.7\% in 2017 and 6.8\% in 2019, with an intermediate 22.8\% in 2018. From 2020 onwards it never falls below 20\%: 34.4\% in 2020, 20--26\% in 2021--2024, and 46.2\% in 2025. The pairwise shares with ES rise in both directions, from under 1\% in 2017 and 2019 to 10.0\% (BTC from ES) and 7.7\% (ES from BTC) in 2025, so that integration is genuinely two-sided at the pairwise level. The net spillover of bitcoin, however, is negative in every year from 2020 to 2025 (between $-1.6$ and $-14.6$), while it was positive in 2016, 2018 and 2019; none of the yearly intervals excludes zero for bitcoin, but the interval for ether excludes zero in 2025 ($-20.2$, interval $-31.4$ to $-4.5$). The total index by year rises from 51--55\% in 2016--2019 to 61--63\% in 2020--2024 and 71.5\% in 2025. | |
| 172 | 129 | |
| 173 | 130 | \begin{table}[htbp] |
| 174 | 131 | \centering |
| 175 | −\caption{Connectedness Table --- Rate-Hiking Regime (2022-01 to 2022-12).} | |
| 176 | −\label{tab:connectedness_ratehikes} | |
| 132 | +\caption{Connectedness by calendar year, log realized volatility, VAR(2), $H = 10$.} | |
| 133 | +\label{tab:yearly} | |
| 134 | +\adjustbox{max width=\textwidth}{% | |
| 177 | 135 | \begin{threeparttable} |
| 178 | −\begin{adjustbox}{max width=\textwidth} | |
| 179 | −\begin{tabular}{@{}l*{10}{r}r@{}} | |
| 180 | −\toprule | |
| 181 | −& ES & NQ & EURUSD & USDJPY & GBPUSD & GC & CL & BTC & ETH & VIX & FROM \\ | |
| 182 | −\midrule | |
| 183 | −ES & 21.9 & 19.5 & 11.7 & 3.8 & 10.0 & 12.2 & 9.4 & 3.9 & 3.4 & 4.3 & 78.1 \\ | |
| 184 | −NQ & 20.7 & 21.7 & 11.5 & 3.6 & 9.4 & 11.8 & 9.9 & 4.2 & 3.6 & 3.7 & 78.4 \\ | |
| 185 | −EURUSD & 11.4 & 11.2 & 22.9 & 8.6 & 17.0 & 13.5 & 10.4 & 2.5 & 1.8 & 0.7 & 77.1 \\ | |
| 186 | −USDJPY & 6.2 & 5.8 & 13.3 & 38.9 & 11.3 & 10.3 & 6.0 & 3.0 & 2.6 & 2.6 & 61.1 \\ | |
| 187 | −GBPUSD & 9.4 & 8.6 & 18.5 & 8.7 & 31.4 & 12.0 & 7.5 & 1.9 & 1.6 & 0.5 & 68.6 \\ | |
| 188 | −GC & 12.9 & 12.0 & 14.2 & 6.7 & 11.1 & 22.1 & 11.5 & 3.9 & 3.8 & 1.9 & 77.9 \\ | |
| 189 | −CL & 11.6 & 11.6 & 12.0 & 5.0 & 8.8 & 13.7 & 30.1 & 2.9 & 2.4 & 1.8 & 69.9 \\ | |
| 190 | −BTC & 3.4 & 2.9 & 1.4 & 1.3 & 0.7 & 2.3 & 1.2 & 43.4 & 38.6 & 4.7 & 56.6 \\ | |
| 191 | −ETH & 3.5 & 3.1 & 1.3 & 1.2 & 0.8 & 2.7 & 1.5 & 38.2 & 43.9 & 3.8 & 56.1 \\ | |
| 192 | −VIX & 5.1 & 3.9 & 2.8 & 4.9 & 2.3 & 3.2 & 2.2 & 4.1 & 3.9 & 67.6 & 32.4 \\ | |
| 193 | −\midrule | |
| 194 | −TO & 84.3 & 78.6 & 86.6 & 43.9 & 71.5 & 81.7 & 59.7 & 64.5 & 61.5 & 23.9 & \textbf{65.6} \\ | |
| 195 | −NET & $+$6.2 & $+$0.2 & $+$9.5 & $-$17.2 & $+$2.8 & $+$3.8 & $-$10.2 & $+$7.9 & $+$5.4 & $-$8.5 & \\ | |
| 196 | −\bottomrule | |
| 197 | −\end{tabular} | |
| 198 | −\end{adjustbox} | |
| 136 | +\input{tables/tab_yearly} | |
| 199 | 137 | \begin{tablenotes}[flushleft] |
| 200 | 138 | \footnotesize |
| 201 | −\item \textit{Notes:} Same methodology as \Cref{tab:connectedness_full}. TSI = 65.62\%. | |
| 139 | +\item \textit{Notes:} 2016 covers 11 March--31 December. TSI in percent and net spillovers in percentage points, with 90\% intervals from 300 bootstrap replications in brackets. ``FROM BTC excl.\ ETH'' is the share of bitcoin's forecast-error variance due to the eight non-crypto instruments. BTC $\leftarrow$ ES is the share of bitcoin's variance due to ES shocks and ES $\leftarrow$ BTC the share of ES variance due to bitcoin shocks. Source: \path{results/rev_table_yearly.csv}. | |
| 202 | 140 | \end{tablenotes} |
| 203 | −\end{threeparttable} | |
| 141 | +\end{threeparttable}} | |
| 204 | 142 | \end{table} |
| 205 | 143 | |
| 206 | −The 2022 regime reveals that \textbf{BTC transitions to a net volatility transmitter} ($+7.9\%$), with ETH also becoming a net transmitter ($+5.4\%$). This marks a significant departure from the pre-COVID period. EURUSD emerges as the largest net transmitter ($+9.5\%$), driven by the EUR/USD depreciation toward parity. The BTC TO spillover of 64.5\% during this regime---compared to 27.0\% pre-COVID---represents a dramatic increase in crypto's influence. | |
| 207 | − | |
| 208 | −\Cref{fig:net_spillovers_regimes} compares net directional spillovers across regimes. | |
| 209 | − | |
| 210 | 144 | \begin{figure}[htbp] |
| 211 | 145 | \centering |
| 212 | −\includegraphics[width=\textwidth]{fig4_net_spillovers_regimes.png} | |
| 213 | −\caption{Net Directional Spillovers by Market Regime.} | |
| 214 | −\label{fig:net_spillovers_regimes} | |
| 146 | +\includegraphics[width=\textwidth]{fig8_yearly_crypto_integration.png} | |
| 147 | +\caption{Bitcoin's integration with traditional assets by calendar year.} | |
| 148 | +\label{fig:yearly_integration} | |
| 215 | 149 | \begin{minipage}{0.95\textwidth} |
| 216 | 150 | \vspace{4pt} |
| 217 | −\footnotesize\textit{Notes:} Net directional spillovers (TO $-$ FROM) for each asset across three regimes. Positive values indicate net transmitters; negative values indicate net receivers. TSI for each regime shown in legend. | |
| 151 | +\footnotesize\textit{Notes:} Panel (a): net directional spillovers of bitcoin and ES by year with 90\% bootstrap intervals. Panel (b): share of bitcoin's 10-day forecast-error variance explained by the eight traditional instruments, and pairwise shares between bitcoin and ES. From \Cref{tab:yearly}. | |
| 218 | 152 | \end{minipage} |
| 219 | 153 | \end{figure} |
| 220 | 154 | |
| 221 | −\subsection{Volatility Hierarchy Evolution and Crypto Integration} | |
| 222 | − | |
| 223 | −\Cref{fig:net_directional_btc_es} presents the rolling 200-day net directional spillovers for BTC and ES. | |
| 155 | +\Cref{fig:net_directional_btc_es} shows the same evolution in rolling windows. Bitcoin's 500-day net spillover drifts from slightly negative in 2018 to a maximum near $+15$ percentage points at the end of 2019, falls through 2020--2021, and remains between $-5$ and $-20$ from 2022 to the end of the sample, finishing at $-19.1$ in March 2026; it is positive in only 27\% of the 500-day windows and 34\% of the 200-day windows. ES is a net transmitter in every window, between $+20$ and $+57$ percentage points. | |
| 224 | 156 | |
| 225 | 157 | \begin{figure}[htbp] |
| 226 | 158 | \centering |
| 227 | 159 | \includegraphics[width=\textwidth]{fig6_net_directional_btc_es.png} |
| 228 | −\caption{Rolling Net Directional Spillovers: BTC vs.\ ES.} | |
| 160 | +\caption{Rolling net directional spillovers of bitcoin and ES.} | |
| 229 | 161 | \label{fig:net_directional_btc_es} |
| 230 | 162 | \begin{minipage}{0.95\textwidth} |
| 231 | 163 | \vspace{4pt} |
| 232 | −\footnotesize\textit{Notes:} Rolling 200-day net directional spillovers for Bitcoin (purple) and E-Mini S\&P 500 (blue). Positive values indicate net transmission. Shaded area distinguishes BTC net transmitter (above zero) from net receiver (below zero) episodes. | |
| 164 | +\footnotesize\textit{Notes:} Net directional spillovers (percentage points) for bitcoin (purple) and ES (blue) from VAR(4) estimates on log realized volatility over rolling windows of 200 (thin lines) and 500 (thick lines) trading days. Vertical lines as in \Cref{fig:rolling_spillover}. Source: \path{results/rev_rolling_w200.csv}, \path{rev_rolling_w500.csv}. | |
| 233 | 165 | \end{minipage} |
| 234 | 166 | \end{figure} |
| 235 | 167 | |
| 236 | −The evolution reveals a gradual but unmistakable trend toward greater crypto integration. In the early period (2017--2018), BTC alternates between small positive and negative net spillovers. During the COVID crash, BTC temporarily becomes a significant net receiver. By late 2025, BTC's rolling net spillover stabilizes at approximately $+4.58\%$, while ES is near-neutral at $-0.62\%$, suggesting a more balanced volatility hierarchy. | |
| 168 | +\subsection{Network Representation} | |
| 169 | +\label{sec:network} | |
| 237 | 170 | |
| 238 | −\subsection{Network Visualization} | |
| 239 | − | |
| 240 | −\Cref{fig:network_graph} presents the volatility transmission network, where directed edges represent pairwise spillovers exceeding the median threshold (5.7\%). | |
| 171 | +\Cref{fig:network_graph} draws the net pairwise directional spillovers of \eqref{eq:net_pairwise} that exceed the 60th percentile of all pairwise values in absolute terms (1.0 percentage point). The graph has a hub-and-spoke structure: ES and NQ send net volatility to every other traditional instrument and to the VIX, the thickest edge being ES $\to$ VIX; EUR/USD sends net volatility to GBP/USD, USD/JPY and gold; and gold sends a small net flow to crude oil. Bitcoin and ether are isolated at this threshold because their net pairwise spillovers with every traditional instrument---and with each other---are smaller than one percentage point in the full sample, even though their gross exposures to equities are not zero. The network therefore summarizes the asymmetric transmission among traditional assets rather than the gross linkages of the crypto block, which \Cref{sec:yearly} shows to be growing. | |
| 241 | 172 | |
| 242 | 173 | \begin{figure}[htbp] |
| 243 | 174 | \centering |
| 244 | −\includegraphics[width=0.85\textwidth]{fig7_network_graph.png} | |
| 245 | −\caption{Volatility Transmission Network.} | |
| 175 | +\includegraphics[width=0.8\textwidth]{fig7_network_graph.png} | |
| 176 | +\caption{Network of net pairwise directional spillovers, full sample.} | |
| 246 | 177 | \label{fig:network_graph} |
| 247 | 178 | \begin{minipage}{0.95\textwidth} |
| 248 | 179 | \vspace{4pt} |
| 249 | −\footnotesize\textit{Notes:} Nodes represent assets, colored by asset class (blue: equity, green: FX, orange: commodity, purple: crypto, brown: VIX). Node size is proportional to total TO spillover. Directed edges represent pairwise GFEVD contributions above the median threshold. Two distinct communities emerge: a densely connected traditional asset core and an isolated crypto cluster. | |
| 180 | +\footnotesize\textit{Notes:} Nodes are the ten instruments, coloured by asset class, with size proportional to TO spillover. A directed edge from $i$ to $j$ is drawn when $\mathrm{NET}_{i \to j}$ exceeds 1.0 percentage point (the 60th percentile of absolute net pairwise spillovers); edge width is proportional to its value. From the decomposition of \Cref{tab:connectedness_full}. | |
| 250 | 181 | \end{minipage} |
| 251 | 182 | \end{figure} |
| 252 | 183 | |
| 253 | −The network reveals a core--periphery architecture: traditional assets form a densely connected core with bidirectional edges, while cryptocurrencies exist as a separate cluster with strong internal connections but no edges crossing to the traditional asset core. VIX occupies a peripheral position, receiving shocks from equities but transmitting little. | |
| 184 | +\subsection{Granger Causality} | |
| 185 | +\label{sec:granger_results} | |
| 254 | 186 | |
| 255 | −\subsection{Trading Session Analysis} | |
| 187 | +\Cref{tab:granger_causality} reports Granger-causality tests on daily log realized volatility with four lags over the common panel. Equity futures Granger-cause the realized volatility of the VIX ($F = 19.9$ for ES and $14.4$ for NQ, $p < 0.001$ under both conventional and HAC inference), and the reverse direction is also significant though weaker ($F = 5.3$ and $5.8$), confirming the asymmetric two-way link of \Cref{sec:full_sample}. ES and NQ do not Granger-cause each other beyond their own lags, which is expected for two indices whose volatilities move almost simultaneously. None of ES, NQ or the VIX Granger-causes bitcoin's realized volatility ($p$ between 0.26 and 0.66). In the other direction, bitcoin Granger-causes the realized volatility of the VIX ($F = 5.1$, $p < 0.001$) and, marginally, of ES ($F = 2.3$, $p = 0.054$; HAC $p = 0.024$), and there is two-way predictability between bitcoin and gold. These statistics must be read with two cautions. The sums of the coefficients on the causing variable are between $-0.07$ and $+0.03$, so that the predictive content, while statistically detectable in a sample of 2{,}500 days, is economically small relative to own-lag persistence. And sixteen tests are reported, so that one or two rejections at the 5\% level would be expected under the global null. The session-ordered regressions of \Cref{sec:sessions} provide a sharper test of the direction of information flow between bitcoin and U.S. equities. | |
| 256 | 188 | |
| 257 | −\Cref{fig:hourly_volatility} displays the average absolute 5-minute return by hour of day (UTC) for VIX, ES, NQ, and BTC. | |
| 189 | +\begin{table}[htbp] | |
| 190 | +\centering | |
| 191 | +\caption{Granger-causality tests on daily log realized volatility, four lags.} | |
| 192 | +\label{tab:granger_causality} | |
| 193 | +\begin{threeparttable} | |
| 194 | +\small | |
| 195 | +\input{tables/tab_granger} | |
| 196 | +\begin{tablenotes}[flushleft] | |
| 197 | +\footnotesize | |
| 198 | +\item \textit{Notes:} Common trading-day panel, 2016-03-11 to 2026-03-11. $F$ is the conventional statistic of \eqref{eq:granger}; Wald (HAC) uses a Newey--West covariance matrix with ten lags and is distributed $\chi^2(4)$ under the null. \sym{***}, \sym{**}, \sym{*}: significant at 1\%, 5\%, 10\%. Source: \path{results/rev_table_granger.csv}. | |
| 199 | +\end{tablenotes} | |
| 200 | +\end{threeparttable} | |
| 201 | +\end{table} | |
| 202 | + | |
| 203 | +\subsection{Intraday Periodicity and Trading Sessions} | |
| 204 | +\label{sec:sessions} | |
| 205 | + | |
| 206 | +\Cref{fig:hourly_volatility} plots the mean absolute 5-minute return by hour of the day in UTC for the VIX, ES, NQ and bitcoin over the common sample, after conversion of the Eastern-time stamps. The equity futures display the familiar pattern of the U.S. cash session \citep{Wood1985,Harris1986}: a trough around 04:00 UTC during the late Asian hours, a rise from 07:00--08:00 UTC when European markets open, a sharp peak in the hour of the U.S. cash open (13:30--14:30 UTC depending on daylight-saving time), a second peak in the hour before the cash close, and a decline after 20:00 UTC. The peak-to-trough ratio is 3.9 for ES and 4.5 for NQ. The VIX, which is disseminated from 07:15--08:15 UTC, is relatively quiet during European hours and three times as volatile in the hour of the U.S. cash open as at its 10:00 UTC minimum; because its ``returns'' are changes in an implied-volatility index, its hourly profile also reflects the option market's reaction to the cash open. Bitcoin's profile is nearly flat: the mean absolute return ranges from 0.240\% at 07:00 UTC to 0.287\% at 18:00 UTC, a peak-to-trough ratio of 1.2, with a mild hump during U.S. hours consistent with \citet{Eross2019}. | |
| 258 | 207 | |
| 259 | 208 | \begin{figure}[htbp] |
| 260 | 209 | \centering |
| 261 | 210 | \includegraphics[width=\textwidth]{fig5_hourly_volatility.png} |
| 262 | −\caption{Intraday Volatility Pattern by Asset and Trading Session.} | |
| 211 | +\caption{Intraday periodicity of absolute 5-minute returns by hour of the day (UTC).} | |
| 263 | 212 | \label{fig:hourly_volatility} |
| 264 | 213 | \begin{minipage}{0.95\textwidth} |
| 265 | 214 | \vspace{4pt} |
| 266 | −\footnotesize\textit{Notes:} Average absolute 5-minute return (\%) by hour of day (UTC). Shaded regions: Asian (00:00--08:00 UTC), European (08:00--14:30 UTC), U.S.\ (14:30--21:00 UTC). Bitcoin's volatility is remarkably uniform across all hours, contrasting with the session-dependent patterns of ES, NQ, and VIX. | |
| 215 | +\footnotesize\textit{Notes:} Mean absolute 5-minute log return (\%) by UTC hour, 11 March 2016 to 11 March 2026, after conversion of the vendor's U.S. Eastern time stamps with daylight-saving rules. Shaded areas mark the Asian (00:00--08:00), European (08:00--14:30) and U.S. (14:30--21:00) sessions. The VIX is disseminated only from 03:15 Eastern time. Source: \path{results/rev_intraday_hourly_absret_utc.csv}. | |
| 267 | 216 | \end{minipage} |
| 268 | 217 | \end{figure} |
| 269 | 218 | |
| 270 | −\textit{Equity futures (ES, NQ)} display a pronounced peak during the European session (09:00--14:00 UTC), reflecting the overlap between European market openings and the lead-up to the U.S.\ cash open. \textit{VIX} shows an even more concentrated pattern, with a sharp peak at 09:00--10:00 UTC. \textit{Bitcoin} exhibits a remarkably flat intraday profile (0.24\%--0.27\%), reflecting its decentralized, globally distributed market structure. | |
| 271 | − | |
| 272 | −\Cref{tab:granger_causality} presents Granger causality test results. | |
| 219 | +\Cref{tab:sessions} translates the profiles into shares of daily variance. The U.S. session generates 53\% of the daily variance of ES and 54\% of NQ, the European session 31--32\%, and the Asian session 14--16\%. For the VIX the U.S. session accounts for 63\% of the variance realized during its dissemination hours. For bitcoin the three sessions contribute 37\%, 25\% and 38\%: the smaller European share reflects the shorter session (6.5 hours against 8 for the Asian session) rather than lower volatility per hour, and the U.S. session is the most volatile per unit of time. Bitcoin's weekend volatility is lower than its weekday volatility but far from negligible: Saturday and Sunday account for 22.1\% of the variance of an average week (28.6\% would correspond to a uniform distribution), and mean annualized realized volatility is 96--99\% on weekend days against 104--106\% on weekdays, in line with the day-of-week effects of \citet{Baur2019}. The earlier version of this paper, which read the Eastern-time stamps as UTC, attributed the equity-futures peak to the European session and the VIX peak to 09:00--10:00 UTC; both statements described the U.S. cash open shifted by four to five hours. | |
| 273 | 220 | |
| 274 | 221 | \begin{table}[htbp] |
| 275 | 222 | \centering |
| 276 | −\caption{Granger Causality Tests for Realized Volatility.} | |
| 277 | −\label{tab:granger_causality} | |
| 223 | +\caption{Volatility by trading session, 2016-03-11 to 2026-03-11.} | |
| 224 | +\label{tab:sessions} | |
| 278 | 225 | \begin{threeparttable} |
| 279 | −\begin{tabular}{@{}llrrll@{}} | |
| 280 | −\toprule | |
| 281 | −Direction & & $F$-stat & $p$-value & Sig. \\ | |
| 282 | −\midrule | |
| 283 | −ES $\to$ VIX & & 19.864 & $<$0.001 & \stmark \\ | |
| 284 | −NQ $\to$ VIX & & 16.708 & $<$0.001 & \stmark \\ | |
| 285 | −VIX $\to$ ES & & 4.303 & 0.002 & \stmark \\ | |
| 286 | −VIX $\to$ NQ & & 4.181 & 0.002 & \stmark \\ | |
| 287 | −ES $\to$ NQ & & 4.449 & 0.001 & \stmark \\ | |
| 288 | −VIX $\to$ BTC & & 1.642 & 0.161 & \\ | |
| 289 | −ES $\to$ BTC & & 0.581 & 0.676 & \\ | |
| 290 | −NQ $\to$ BTC & & 0.441 & 0.779 & \\ | |
| 291 | −BTC $\to$ VIX & & 1.796 & 0.127 & \\ | |
| 292 | −\bottomrule | |
| 293 | −\end{tabular} | |
| 226 | +\small | |
| 227 | +\input{tables/tab_sessions} | |
| 294 | 228 | \begin{tablenotes}[flushleft] |
| 295 | 229 | \footnotesize |
| 296 | −\item \textit{Notes:} Granger causality tests with 4 lags applied to daily realized volatility series. \sym{***}~Significant at 1\%. The dominant direction is ES $\to$ VIX ($F=19.86$), confirming that equity futures lead VIX. All BTC pairings are insignificant. | |
| 230 | +\item \textit{Notes:} Weekdays only. Mean $|r|$ is the average absolute 5-minute return in the session; annualized volatility is the mean over days of $\sqrt{252 \cdot \RV^{s}_{i,t}}$, where $\RV^{s}_{i,t}$ is the session realized variance of \eqref{eq:session_rv}; share of day is the mean over days of the session's share of the variance realized in the three sessions. The VIX has no Asian-session bars except a few minutes before 08:00 UTC in winter. Source: \path{results/rev_intraday_sessions.csv}. | |
| 297 | 231 | \end{tablenotes} |
| 298 | 232 | \end{threeparttable} |
| 299 | 233 | \end{table} |
| 300 | 234 | |
| 301 | −The strongest causal relationship runs from ES to VIX ($F = 19.86$, $p < 0.001$), confirming that equity futures are the primary drivers of VIX movements. The reverse direction (VIX $\to$ ES) is significant but weaker ($F = 4.30$), suggesting bidirectional but asymmetric causality. All pairwise tests involving BTC are insignificant at the 5\% level, reinforcing the network analysis finding that crypto volatility operates independently of traditional market dynamics in the full sample. | |
| 235 | +\Cref{tab:sessions_predictive} reports the session-ordered predictive regressions of \eqref{eq:session_predictive}. Bitcoin's Asian- and European-session variance does not help predict the U.S.-session variance of ES or NQ on the same day once four lags of the latter are included: the HAC Wald statistics have $p$-values between 0.16 and 0.48 and the incremental $R^2$ is below 0.0012. Bitcoin's earlier-session variance does predict the U.S.-session variance of the VIX ($p < 0.001$), but the incremental $R^2$ is 0.007 and the same-day coefficient is 0.06. In the reverse direction the evidence is stronger and uniform: the previous day's U.S.-session variance of ES, NQ and the VIX predicts bitcoin's Asian-session variance with coefficients of 0.08--0.10 and $p$-values below 0.002, and ES's own Asian-session (Globex overnight) variance predicts bitcoin's U.S.-session variance. For comparison, ES's overnight variance predicts its own U.S.-session variance with a coefficient of 0.38 and an incremental $R^2$ of 0.046, an order of magnitude larger than any cross-asset effect. | |
| 236 | + | |
| 237 | +\begin{table}[htbp] | |
| 238 | +\centering | |
| 239 | +\caption{Session-ordered predictive regressions for log session realized variance.} | |
| 240 | +\label{tab:sessions_predictive} | |
| 241 | +\adjustbox{max width=\textwidth}{% | |
| 242 | +\begin{threeparttable} | |
| 243 | +\input{tables/tab_sessions_predictive} | |
| 244 | +\begin{tablenotes}[flushleft] | |
| 245 | +\footnotesize | |
| 246 | +\item \textit{Notes:} Each row is a regression of the log realized variance of the target session on four lags of itself and on the log realized variance of the predictor session on the same day and three previous days, \eqref{eq:session_predictive}. ``Coef.\ (same day)'' is $\hat{\gamma}_0$ with its HAC standard error; Wald (HAC) tests the joint nullity of the four predictor coefficients and is $\chi^2(4)$ under the null (Newey--West, ten lags); $\Delta R^2$ is the increase in $R^2$ relative to the own-lags regression. In ``(t$-$1)'' rows the predictor is the U.S. session of the previous trading day. \sym{***}, \sym{**}, \sym{*}: significant at 1\%, 5\%, 10\%. Source: \path{results/rev_intraday_session_predictive.csv}. | |
| 247 | +\end{tablenotes} | |
| 248 | +\end{threeparttable}} | |
| 249 | +\end{table} | |
| 250 | + | |
| 251 | +\Cref{tab:weekend_btc} addresses the specific hypothesis that bitcoin's weekend trading provides a continuous information channel for Monday equity volatility. Regressing the log U.S.-session variance of ES on Mondays on Friday's ES and bitcoin variances, the addition of bitcoin's Saturday--Sunday variance has a coefficient of $-0.04$ (standard error 0.05) and raises $R^2$ by less than 0.001; adding bitcoin's Monday Asian-session variance leaves both crypto coefficients insignificant at the 5\% level. Over 501 Mondays, weekend bitcoin volatility carries no detectable incremental information about the volatility of the U.S. equity market when it reopens. | |
| 252 | + | |
| 253 | +\begin{table}[htbp] | |
| 254 | +\centering | |
| 255 | +\caption{Does weekend bitcoin volatility predict Monday U.S.-session volatility of ES?} | |
| 256 | +\label{tab:weekend_btc} | |
| 257 | +\adjustbox{max width=\textwidth}{% | |
| 258 | +\begin{threeparttable} | |
| 259 | +\input{tables/tab_weekend_btc} | |
| 260 | +\begin{tablenotes}[flushleft] | |
| 261 | +\footnotesize | |
| 262 | +\item \textit{Notes:} Dependent variable: log U.S.-session realized variance of ES on Mondays, 2016--2026. Regressors: log Friday U.S.-session variance of ES, log Friday daily variance of bitcoin (coefficient not shown), log Saturday-plus-Sunday variance of bitcoin and log Monday Asian-session variance of bitcoin. HAC standard errors (four lags) in parentheses. \sym{***}, \sym{**}, \sym{*}: significant at 1\%, 5\%, 10\%. Source: \path{results/rev_intraday_weekend_btc_monday_es.csv}. | |
| 263 | +\end{tablenotes} | |
| 264 | +\end{threeparttable}} | |
| 265 | +\end{table} | |
added
paper/tables/tab_audit_construction.tex
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@@ -0,0 +1,9 @@ | ||
| 1 | +\begin{tabular}{@{}lrrrrrrr@{}} | |
| 2 | +\toprule | |
| 3 | +Construction of the panel & $T$ & TSI & ES & NQ & VIX & BTC & USDJPY \\ | |
| 4 | +\midrule | |
| 5 | +Original: calendar days, forward-filled, RV levels & 3651 & 55.4 & $+$26.8 & $+$19.7 & $-$23.4 & $+$1.2 & $-$5.0 \\ | |
| 6 | +Trading days, RV levels & 2514 & 50.0 & $+$41.6 & $+$29.8 & $-$23.4 & $+$1.6 & $-$8.0 \\ | |
| 7 | +Trading days, log RV (revised baseline) & 2514 & 54.8 & $+$35.9 & $+$25.6 & $-$20.6 & $+$1.7 & $-$5.2 \\ | |
| 8 | +\bottomrule | |
| 9 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_connectedness_full.tex
+33 −0
@@ -0,0 +1,33 @@ | ||
| 1 | +\begin{tabular}{@{}l*{10}{r}r@{}} | |
| 2 | +\toprule | |
| 3 | +& \multicolumn{10}{c}{Shock origin $j$} & \\ | |
| 4 | +\cmidrule(lr){2-11} | |
| 5 | +Recipient $i$ & ES & NQ & EURUSD & USDJPY & GBPUSD & GC & CL & BTC & ETH & VIX & FROM \\ | |
| 6 | +\midrule | |
| 7 | +ES & \textbf{31.9} & 28.3 & 5.4 & 4.8 & 4.2 & 6.1 & 5.5 & 1.3 & 0.6 & 11.9 & 68.1 \\ | |
| 8 | + & & & & & & & & & & & {\scriptsize[66.7, 69.8]} \\ | |
| 9 | +NQ & 30.1 & \textbf{33.7} & 4.7 & 4.3 & 3.7 & 5.8 & 4.8 & 1.1 & 0.5 & 11.3 & 66.3 \\ | |
| 10 | + & & & & & & & & & & & {\scriptsize[64.8, 68.2]} \\ | |
| 11 | +EURUSD & 9.1 & 8.0 & \textbf{35.5} & 14.3 & 16.5 & 10.0 & 3.9 & 0.4 & 0.3 & 2.0 & 64.5 \\ | |
| 12 | + & & & & & & & & & & & {\scriptsize[62.2, 67.0]} \\ | |
| 13 | +USDJPY & 8.5 & 7.5 & 15.2 & \textbf{44.5} & 9.1 & 9.0 & 3.5 & 0.4 & 0.3 & 2.1 & 55.5 \\ | |
| 14 | + & & & & & & & & & & & {\scriptsize[52.5, 58.9]} \\ | |
| 15 | +GBPUSD & 8.9 & 7.5 & 19.3 & 10.2 & \textbf{40.1} & 7.1 & 3.5 & 0.6 & 0.8 & 1.8 & 59.9 \\ | |
| 16 | + & & & & & & & & & & & {\scriptsize[56.7, 63.1]} \\ | |
| 17 | +GC & 11.0 & 9.4 & 11.4 & 9.8 & 6.3 & \textbf{41.4} & 5.7 & 0.6 & 0.6 & 4.0 & 58.6 \\ | |
| 18 | + & & & & & & & & & & & {\scriptsize[55.8, 61.6]} \\ | |
| 19 | +CL & 12.2 & 10.4 & 3.9 & 3.8 & 2.8 & 6.8 & \textbf{53.9} & 0.8 & 0.9 & 4.5 & 46.1 \\ | |
| 20 | + & & & & & & & & & & & {\scriptsize[40.5, 52.4]} \\ | |
| 21 | +BTC & 1.8 & 1.5 & 0.4 & 0.2 & 0.5 & 0.4 & 0.4 & \textbf{66.7} & 27.0 & 1.1 & 33.3 \\ | |
| 22 | + & & & & & & & & & & & {\scriptsize[30.5, 37.8]} \\ | |
| 23 | +ETH & 1.4 & 0.9 & 0.6 & 0.3 & 1.1 & 1.4 & 0.8 & 27.9 & \textbf{64.9} & 0.8 & 35.1 \\ | |
| 24 | + & & & & & & & & & & & {\scriptsize[32.0, 39.8]} \\ | |
| 25 | +VIX & 21.2 & 18.5 & 3.3 & 2.5 & 2.4 & 4.9 & 3.8 & 2.1 & 1.5 & \textbf{39.9} & 60.1 \\ | |
| 26 | + & & & & & & & & & & & {\scriptsize[57.7, 62.7]} \\ | |
| 27 | +\midrule | |
| 28 | +TO & 104.1 & 91.9 & 64.1 & 50.2 & 46.6 & 51.4 & 31.8 & 35.1 & 32.7 & 39.5 & \textbf{54.8} \\ | |
| 29 | + & {\scriptsize[98.3, 109.1]} & {\scriptsize[86.2, 96.9]} & {\scriptsize[58.7, 70.5]} & {\scriptsize[45.4, 56.0]} & {\scriptsize[41.7, 52.8]} & {\scriptsize[46.0, 58.3]} & {\scriptsize[26.1, 37.7]} & {\scriptsize[31.5, 39.6]} & {\scriptsize[29.0, 37.4]} & {\scriptsize[34.6, 46.2]} & {\scriptsize[53.1, 56.9]} \\ | |
| 30 | +NET & $+$35.9 & $+$25.6 & $-$0.4 & $-$5.2 & $-$13.2 & $-$7.2 & $-$14.2 & $+$1.7 & $-$2.4 & $-$20.6 & \\ | |
| 31 | + & {\scriptsize[$+$29.9, $+$41.5]} & {\scriptsize[$+$19.0, $+$31.3]} & {\scriptsize[$-$6.0, $+$5.8]} & {\scriptsize[$-$10.2, $+$0.2]} & {\scriptsize[$-$18.0, $-$7.4]} & {\scriptsize[$-$12.5, $-$0.8]} & {\scriptsize[$-$21.6, $-$6.7]} & {\scriptsize[$-$3.3, $+$6.4]} & {\scriptsize[$-$7.9, $+$2.1]} & {\scriptsize[$-$25.2, $-$14.0]} & \\ | |
| 32 | +\bottomrule | |
| 33 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_granger.tex
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@@ -0,0 +1,22 @@ | ||
| 1 | +\begin{tabular}{@{}llrrrrr@{}} | |
| 2 | +\toprule | |
| 3 | +Cause & Effect & $T$ & $F$ & $p$ & Wald (HAC) & $p$ \\ | |
| 4 | +\midrule | |
| 5 | +ES & VIX & 2510 & 19.94$^{***}$ & 0.000 & 62.78$^{***}$ & 0.000 \\ | |
| 6 | +NQ & VIX & 2510 & 14.40$^{***}$ & 0.000 & 48.88$^{***}$ & 0.000 \\ | |
| 7 | +VIX & ES & 2510 & 5.33$^{***}$ & 0.000 & 22.21$^{***}$ & 0.000 \\ | |
| 8 | +VIX & NQ & 2510 & 5.83$^{***}$ & 0.000 & 22.18$^{***}$ & 0.000 \\ | |
| 9 | +ES & NQ & 2510 & 1.10 & 0.354 & 4.84 & 0.304 \\ | |
| 10 | +NQ & ES & 2510 & 0.62 & 0.647 & 2.02 & 0.732 \\ | |
| 11 | +ES & BTC & 2510 & 1.33 & 0.257 & 6.29 & 0.178 \\ | |
| 12 | +NQ & BTC & 2510 & 1.17 & 0.324 & 4.77 & 0.312 \\ | |
| 13 | +VIX & BTC & 2510 & 0.60 & 0.663 & 2.32 & 0.677 \\ | |
| 14 | +BTC & ES & 2510 & 2.33$^{*}$ & 0.054 & 11.21$^{**}$ & 0.024 \\ | |
| 15 | +BTC & NQ & 2510 & 1.47 & 0.208 & 6.65 & 0.155 \\ | |
| 16 | +BTC & VIX & 2510 & 5.10$^{***}$ & 0.000 & 24.46$^{***}$ & 0.000 \\ | |
| 17 | +USDJPY & ES & 2510 & 3.50$^{***}$ & 0.007 & 13.69$^{***}$ & 0.008 \\ | |
| 18 | +ES & USDJPY & 2510 & 1.59 & 0.174 & 5.77 & 0.217 \\ | |
| 19 | +GC & BTC & 2510 & 3.80$^{***}$ & 0.004 & 15.32$^{***}$ & 0.004 \\ | |
| 20 | +BTC & GC & 2510 & 6.44$^{***}$ & 0.000 & 33.08$^{***}$ & 0.000 \\ | |
| 21 | +\bottomrule | |
| 22 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_lag_selection.tex
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@@ -0,0 +1,9 @@ | ||
| 1 | +\begin{tabular}{@{}lrrrrrrrrrr@{}} | |
| 2 | +\toprule | |
| 3 | +Criterion & $p=1$ & $p=2$ & $p=3$ & $p=4$ & $p=5$ & $p=6$ & $p=7$ & $p=8$ & $p=9$ & $p=10$ \\ | |
| 4 | +\midrule | |
| 5 | +AIC & -30.42 & -31.16 & -31.45 & -31.58 & \textbf{-31.63} & -31.62 & -31.60 & -31.60 & -31.58 & -31.57 \\ | |
| 6 | +BIC & -30.17 & -30.67 & \textbf{-30.73} & -30.62 & -30.44 & -30.20 & -29.95 & -29.71 & -29.47 & -29.22 \\ | |
| 7 | +HQ & -30.33 & -30.98 & -31.19 & \textbf{-31.23} & -31.20 & -31.11 & -31.00 & -30.91 & -30.82 & -30.72 \\ | |
| 8 | +\bottomrule | |
| 9 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_regime_covid_crash.tex
+21 −0
@@ -0,0 +1,21 @@ | ||
| 1 | +\begin{tabular}{@{}l*{10}{r}r@{}} | |
| 2 | +\toprule | |
| 3 | +& \multicolumn{10}{c}{Shock origin $j$} & \\ | |
| 4 | +\cmidrule(lr){2-11} | |
| 5 | +Recipient $i$ & ES & NQ & EURUSD & USDJPY & GBPUSD & GC & CL & BTC & ETH & VIX & FROM \\ | |
| 6 | +\midrule | |
| 7 | +ES & \textbf{20.2} & 20.4 & 9.8 & 18.5 & 8.4 & 8.1 & 2.2 & 5.3 & 2.4 & 4.7 & 79.8 \\ | |
| 8 | +NQ & 18.9 & \textbf{21.0} & 9.3 & 18.4 & 7.4 & 8.2 & 2.7 & 6.1 & 3.1 & 4.8 & 79.0 \\ | |
| 9 | +EURUSD & 10.4 & 11.8 & \textbf{20.3} & 23.0 & 13.5 & 9.0 & 2.4 & 5.3 & 3.2 & 1.0 & 79.7 \\ | |
| 10 | +USDJPY & 10.4 & 11.1 & 12.9 & \textbf{36.8} & 10.3 & 7.8 & 0.7 & 5.4 & 3.4 & 1.1 & 63.2 \\ | |
| 11 | +GBPUSD & 11.2 & 11.9 & 13.9 & 17.4 & \textbf{22.2} & 9.4 & 2.4 & 7.5 & 3.3 & 0.8 & 77.8 \\ | |
| 12 | +GC & 12.1 & 13.3 & 9.3 & 16.0 & 6.3 & \textbf{22.5} & 5.0 & 8.8 & 5.4 & 1.3 & 77.5 \\ | |
| 13 | +CL & 8.1 & 9.0 & 4.1 & 2.3 & 2.0 & 20.8 & \textbf{47.6} & 1.9 & 3.1 & 1.2 & 52.4 \\ | |
| 14 | +BTC & 8.0 & 10.2 & 7.6 & 15.4 & 5.9 & 7.9 & 4.3 & \textbf{24.9} & 13.9 & 2.0 & 75.1 \\ | |
| 15 | +ETH & 5.2 & 7.8 & 6.5 & 15.8 & 4.7 & 4.5 & 1.9 & 18.1 & \textbf{33.4} & 2.0 & 66.6 \\ | |
| 16 | +VIX & 15.0 & 16.6 & 7.1 & 18.0 & 3.2 & 0.5 & 1.8 & 2.3 & 1.0 & \textbf{34.5} & 65.5 \\ | |
| 17 | +\midrule | |
| 18 | +TO & 99.3 & 112.3 & 80.5 & 145.0 & 61.8 & 76.2 & 23.4 & 60.7 & 38.6 & 18.9 & \textbf{71.7} \\ | |
| 19 | +NET & $+$19.4 & $+$33.3 & $+$0.7 & $+$81.8 & $-$16.0 & $-$1.3 & $-$29.0 & $-$14.4 & $-$27.9 & $-$46.6 & \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_regime_precovid.tex
+21 −0
@@ -0,0 +1,21 @@ | ||
| 1 | +\begin{tabular}{@{}l*{10}{r}r@{}} | |
| 2 | +\toprule | |
| 3 | +& \multicolumn{10}{c}{Shock origin $j$} & \\ | |
| 4 | +\cmidrule(lr){2-11} | |
| 5 | +Recipient $i$ & ES & NQ & EURUSD & USDJPY & GBPUSD & GC & CL & BTC & ETH & VIX & FROM \\ | |
| 6 | +\midrule | |
| 7 | +ES & \textbf{26.9} & 27.1 & 3.2 & 14.2 & 0.7 & 5.6 & 6.0 & 0.7 & 0.1 & 15.6 & 73.1 \\ | |
| 8 | +NQ & 26.2 & \textbf{29.0} & 3.2 & 13.6 & 0.6 & 5.4 & 6.4 & 0.8 & 0.1 & 14.8 & 71.0 \\ | |
| 9 | +EURUSD & 11.8 & 12.3 & \textbf{31.6} & 12.0 & 11.1 & 10.1 & 5.1 & 0.2 & 0.4 & 5.5 & 68.4 \\ | |
| 10 | +USDJPY & 18.5 & 19.3 & 7.3 & \textbf{23.9} & 2.0 & 10.6 & 6.7 & 1.1 & 0.4 & 10.1 & 76.1 \\ | |
| 11 | +GBPUSD & 8.5 & 7.1 & 13.5 & 5.9 & \textbf{49.0} & 4.8 & 2.4 & 0.8 & 2.0 & 5.8 & 51.0 \\ | |
| 12 | +GC & 11.1 & 12.0 & 7.3 & 16.3 & 1.6 & \textbf{31.2} & 6.8 & 5.4 & 2.6 & 5.6 & 68.8 \\ | |
| 13 | +CL & 15.9 & 18.7 & 1.7 & 12.5 & 1.2 & 6.0 & \textbf{32.5} & 3.2 & 1.5 & 6.8 & 67.5 \\ | |
| 14 | +BTC & 1.3 & 1.0 & 3.8 & 0.6 & 1.3 & 1.9 & 2.0 & \textbf{74.5} & 13.0 & 0.6 & 25.5 \\ | |
| 15 | +ETH & 0.8 & 0.7 & 1.3 & 0.6 & 2.5 & 0.6 & 0.8 & 24.6 & \textbf{67.5} & 0.6 & 32.5 \\ | |
| 16 | +VIX & 20.4 & 19.9 & 2.3 & 9.7 & 0.9 & 5.3 & 3.9 & 1.4 & 1.0 & \textbf{35.2} & 64.8 \\ | |
| 17 | +\midrule | |
| 18 | +TO & 114.4 & 118.1 & 43.7 & 85.4 & 22.0 & 50.3 & 40.2 & 38.3 & 21.1 & 65.4 & \textbf{59.9} \\ | |
| 19 | +NET & $+$41.3 & $+$47.0 & $-$24.8 & $+$9.3 & $-$29.0 & $-$18.5 & $-$27.3 & $+$12.7 & $-$11.4 & $+$0.6 & \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_regime_rate_hikes.tex
+21 −0
@@ -0,0 +1,21 @@ | ||
| 1 | +\begin{tabular}{@{}l*{10}{r}r@{}} | |
| 2 | +\toprule | |
| 3 | +& \multicolumn{10}{c}{Shock origin $j$} & \\ | |
| 4 | +\cmidrule(lr){2-11} | |
| 5 | +Recipient $i$ & ES & NQ & EURUSD & USDJPY & GBPUSD & GC & CL & BTC & ETH & VIX & FROM \\ | |
| 6 | +\midrule | |
| 7 | +ES & \textbf{29.2} & 23.6 & 8.1 & 2.0 & 7.6 & 9.4 & 3.2 & 3.4 & 3.4 & 10.2 & 70.8 \\ | |
| 8 | +NQ & 27.2 & \textbf{27.6} & 7.4 & 2.2 & 7.1 & 9.1 & 2.9 & 3.4 & 3.7 & 9.4 & 72.4 \\ | |
| 9 | +EURUSD & 10.1 & 8.2 & \textbf{28.7} & 7.8 & 20.7 & 11.7 & 4.5 & 2.1 & 2.3 & 3.9 & 71.3 \\ | |
| 10 | +USDJPY & 3.9 & 3.5 & 12.9 & \textbf{46.3} & 13.3 & 8.6 & 3.5 & 3.1 & 3.1 & 1.7 & 53.7 \\ | |
| 11 | +GBPUSD & 9.1 & 6.5 & 19.0 & 9.4 & \textbf{36.5} & 10.7 & 2.3 & 1.6 & 1.6 & 3.3 & 63.5 \\ | |
| 12 | +GC & 12.2 & 9.8 & 10.8 & 5.3 & 9.5 & \textbf{26.8} & 7.2 & 5.9 & 5.8 & 6.8 & 73.2 \\ | |
| 13 | +CL & 6.6 & 4.1 & 6.4 & 2.5 & 3.0 & 14.6 & \textbf{45.4} & 4.8 & 4.8 & 7.9 & 54.6 \\ | |
| 14 | +BTC & 7.0 & 6.0 & 2.1 & 1.5 & 2.1 & 5.6 & 2.5 & \textbf{35.8} & 33.2 & 4.1 & 64.2 \\ | |
| 15 | +ETH & 6.8 & 6.0 & 1.9 & 1.5 & 2.0 & 5.4 & 3.0 & 31.6 & \textbf{38.8} & 2.9 & 61.2 \\ | |
| 16 | +VIX & 13.3 & 11.0 & 6.7 & 2.9 & 7.2 & 6.8 & 4.1 & 4.8 & 4.1 & \textbf{39.1} & 60.9 \\ | |
| 17 | +\midrule | |
| 18 | +TO & 96.2 & 78.7 & 75.2 & 35.1 & 72.5 & 82.0 & 33.1 & 60.8 & 61.9 & 50.2 & \textbf{64.6} \\ | |
| 19 | +NET & $+$25.4 & $+$6.3 & $+$3.9 & $-$18.6 & $+$9.0 & $+$8.8 & $-$21.5 & $-$3.4 & $+$0.8 & $-$10.7 & \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_regime_spotetf_era.tex
+21 −0
@@ -0,0 +1,21 @@ | ||
| 1 | +\begin{tabular}{@{}l*{10}{r}r@{}} | |
| 2 | +\toprule | |
| 3 | +& \multicolumn{10}{c}{Shock origin $j$} & \\ | |
| 4 | +\cmidrule(lr){2-11} | |
| 5 | +Recipient $i$ & ES & NQ & EURUSD & USDJPY & GBPUSD & GC & CL & BTC & ETH & VIX & FROM \\ | |
| 6 | +\midrule | |
| 7 | +ES & \textbf{25.0} & 24.1 & 7.0 & 4.8 & 6.5 & 6.2 & 3.8 & 4.7 & 3.5 & 14.4 & 75.0 \\ | |
| 8 | +NQ & 24.4 & \textbf{26.1} & 6.0 & 4.9 & 6.0 & 5.7 & 3.8 & 5.3 & 3.9 & 13.9 & 73.9 \\ | |
| 9 | +EURUSD & 10.2 & 9.0 & \textbf{31.5} & 11.7 & 19.5 & 7.4 & 3.6 & 1.1 & 1.4 & 4.6 & 68.5 \\ | |
| 10 | +USDJPY & 9.3 & 10.5 & 13.3 & \textbf{37.6} & 11.5 & 5.1 & 3.6 & 1.9 & 2.0 & 5.2 & 62.4 \\ | |
| 11 | +GBPUSD & 10.3 & 9.6 & 21.4 & 10.3 & \textbf{27.4} & 8.1 & 4.3 & 1.8 & 1.9 & 5.0 & 72.6 \\ | |
| 12 | +GC & 7.7 & 6.9 & 11.0 & 6.1 & 9.5 & \textbf{45.0} & 5.1 & 2.4 & 1.9 & 4.3 & 55.0 \\ | |
| 13 | +CL & 8.6 & 8.8 & 6.4 & 3.7 & 4.6 & 8.9 & \textbf{47.8} & 2.4 & 1.6 & 7.3 & 52.2 \\ | |
| 14 | +BTC & 7.5 & 7.9 & 2.0 & 1.8 & 3.1 & 4.9 & 2.8 & \textbf{40.1} & 24.7 & 5.3 & 59.9 \\ | |
| 15 | +ETH & 7.0 & 7.2 & 4.2 & 3.8 & 4.5 & 6.2 & 1.6 & 24.2 & \textbf{35.8} & 5.5 & 64.2 \\ | |
| 16 | +VIX & 19.3 & 18.7 & 6.0 & 4.1 & 5.6 & 6.6 & 3.7 & 3.6 & 3.7 & \textbf{28.6} & 71.4 \\ | |
| 17 | +\midrule | |
| 18 | +TO & 104.3 & 102.5 & 77.4 & 51.1 & 70.8 & 59.1 & 32.2 & 47.5 & 44.7 & 65.4 & \textbf{65.5} \\ | |
| 19 | +NET & $+$29.4 & $+$28.7 & $+$8.9 & $-$11.3 & $-$1.8 & $+$4.1 & $-$19.9 & $-$12.4 & $-$19.5 & $-$6.0 & \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_regimes.tex
+33 −0
@@ -0,0 +1,33 @@ | ||
| 1 | +\begin{tabular}{@{}lrrrr@{}} | |
| 2 | +\toprule | |
| 3 | + & Pre-COVID & COVID crash & Rate hikes & Spot-ETF era \\ | |
| 4 | + & {\scriptsize 2019-01 to 2020-02} & {\scriptsize 2020-03 to 2020-06} & {\scriptsize 2022-01 to 2022-12} & {\scriptsize 2024-01 to 2026-03} \\ | |
| 5 | +\midrule | |
| 6 | +$T$ (trading days) & 292 & 85 & 254 & 544 \\ | |
| 7 | +VAR lag $p$ & 4 & 1 & 4 & 4 \\ | |
| 8 | +TSI (\%) & 59.9 & 71.7 & 64.6 & 65.5 \\ | |
| 9 | + & {\scriptsize[58.9, 65.7]} & {\scriptsize[65.9, 78.1]} & {\scriptsize[63.7, 70.5]} & {\scriptsize[63.4, 69.3]} \\ | |
| 10 | +\midrule | |
| 11 | +\multicolumn{5}{@{}l}{\textit{Net directional spillovers (pp)}} \\ | |
| 12 | +ES & $+$41.3 & $+$19.4 & $+$25.4 & $+$29.4 \\ | |
| 13 | + & {\scriptsize[$+$23.0, $+$55.6]} & {\scriptsize[$-$23.3, $+$52.1]} & {\scriptsize[$+$8.2, $+$36.7]} & {\scriptsize[$+$18.4, $+$37.9]} \\ | |
| 14 | +NQ & $+$47.0 & $+$33.3 & $+$6.3 & $+$28.7 \\ | |
| 15 | + & {\scriptsize[$+$26.4, $+$60.5]} & {\scriptsize[$-$12.7, $+$63.5]} & {\scriptsize[$-$6.9, $+$18.8]} & {\scriptsize[$+$16.3, $+$37.6]} \\ | |
| 16 | +EURUSD & $-$24.8 & $+$0.7 & $+$3.9 & $+$8.9 \\ | |
| 17 | + & {\scriptsize[$-$35.6, $-$3.3]} & {\scriptsize[$-$29.1, $+$37.3]} & {\scriptsize[$-$7.5, $+$18.4]} & {\scriptsize[$-$2.4, $+$19.4]} \\ | |
| 18 | +USDJPY & $+$9.3 & $+$81.8 & $-$18.6 & $-$11.3 \\ | |
| 19 | + & {\scriptsize[$-$5.7, $+$30.1]} & {\scriptsize[$+$7.3, $+$135.3]} & {\scriptsize[$-$29.2, $-$4.1]} & {\scriptsize[$-$22.5, $+$0.8]} \\ | |
| 20 | +GBPUSD & $-$29.0 & $-$16.0 & $+$9.0 & $-$1.8 \\ | |
| 21 | + & {\scriptsize[$-$42.5, $-$7.7]} & {\scriptsize[$-$41.7, $+$27.4]} & {\scriptsize[$-$3.8, $+$20.8]} & {\scriptsize[$-$12.3, $+$10.0]} \\ | |
| 22 | +GC & $-$18.5 & $-$1.3 & $+$8.8 & $+$4.1 \\ | |
| 23 | + & {\scriptsize[$-$32.4, $+$2.2]} & {\scriptsize[$-$38.0, $+$39.4]} & {\scriptsize[$-$3.6, $+$22.3]} & {\scriptsize[$-$9.5, $+$17.0]} \\ | |
| 24 | +CL & $-$27.3 & $-$29.0 & $-$21.5 & $-$19.9 \\ | |
| 25 | + & {\scriptsize[$-$40.3, $-$3.3]} & {\scriptsize[$-$52.1, $+$12.0]} & {\scriptsize[$-$33.5, $-$5.0]} & {\scriptsize[$-$31.4, $-$4.6]} \\ | |
| 26 | +BTC & $+$12.7 & $-$14.4 & $-$3.4 & $-$12.4 \\ | |
| 27 | + & {\scriptsize[$-$14.8, $+$24.0]} & {\scriptsize[$-$45.9, $+$32.9]} & {\scriptsize[$-$16.7, $+$12.4]} & {\scriptsize[$-$20.4, $-$2.1]} \\ | |
| 28 | +ETH & $-$11.4 & $-$27.9 & $+$0.8 & $-$19.5 \\ | |
| 29 | + & {\scriptsize[$-$27.1, $+$1.7]} & {\scriptsize[$-$54.2, $+$19.1]} & {\scriptsize[$-$12.0, $+$14.3]} & {\scriptsize[$-$27.7, $-$9.2]} \\ | |
| 30 | +VIX & $+$0.6 & $-$46.6 & $-$10.7 & $-$6.0 \\ | |
| 31 | + & {\scriptsize[$-$19.2, $+$23.1]} & {\scriptsize[$-$61.4, $-$11.2]} & {\scriptsize[$-$24.1, $+$4.6]} & {\scriptsize[$-$17.3, $+$8.7]} \\ | |
| 32 | +\bottomrule | |
| 33 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_robustness.tex
+21 −0
@@ -0,0 +1,21 @@ | ||
| 1 | +\begin{tabular}{@{}lrrrrrrrrr@{}} | |
| 2 | +\toprule | |
| 3 | +Specification & $T$ & TSI & ES & NQ & USDJPY & CL & BTC & VIX & BTC own \\ | |
| 4 | +\midrule | |
| 5 | +Baseline: log RV, trading days, VAR(4), H = 10 & 2514 & 54.8 & $+$35.9 & $+$25.6 & $-$5.2 & $-$14.2 & $+$1.7 & $-$20.6 & 66.7 \\ | |
| 6 | +RV in levels (trading days) & 2514 & 50.0 & $+$41.6 & $+$29.8 & $-$8.0 & $-$15.6 & $+$1.6 & $-$23.4 & 74.8 \\ | |
| 7 | +VAR(1) & 2514 & 53.7 & $+$38.6 & $+$26.2 & $-$5.4 & $-$5.8 & $+$7.4 & $-$27.4 & 69.8 \\ | |
| 8 | +VAR(2) & 2514 & 54.1 & $+$36.6 & $+$25.9 & $-$4.9 & $-$7.3 & $+$3.5 & $-$26.1 & 69.5 \\ | |
| 9 | +VAR(3) & 2514 & 54.9 & $+$36.0 & $+$25.5 & $-$5.1 & $-$10.0 & $+$2.7 & $-$24.2 & 68.3 \\ | |
| 10 | +VAR(6) & 2514 & 55.5 & $+$35.0 & $+$23.7 & $-$5.6 & $-$14.8 & $+$1.3 & $-$16.7 & 65.3 \\ | |
| 11 | +H = 5 & 2514 & 54.4 & $+$32.5 & $+$22.7 & $-$5.7 & $-$11.9 & $-$0.3 & $-$17.0 & 66.1 \\ | |
| 12 | +H = 20 & 2514 & 55.3 & $+$39.8 & $+$28.8 & $-$5.4 & $-$17.4 & $+$4.4 & $-$23.3 & 67.3 \\ | |
| 13 | +Weekend-inclusive crypto RV & 2514 & 54.9 & $+$36.3 & $+$26.0 & $-$5.1 & $-$14.6 & $+$0.3 & $-$20.9 & 65.7 \\ | |
| 14 | +Sample 2018-01 to 2026-03 & 2063 & 57.4 & $+$35.7 & $+$27.7 & $-$7.7 & $-$17.3 & $+$3.3 & $-$19.0 & 61.6 \\ | |
| 15 | +Sample 2016-03 to 2019-12 & 954 & 51.5 & $+$35.8 & $+$23.9 & $+$9.9 & $-$8.9 & $+$3.0 & $-$14.4 & 77.6 \\ | |
| 16 | +Sample 2020-01 to 2026-03 & 1560 & 60.9 & $+$36.4 & $+$28.2 & $-$11.3 & $-$16.3 & $-$8.7 & $-$19.5 & 47.7 \\ | |
| 17 | +Excluding VIX & 2514 & 52.9 & $+$26.3 & $+$18.1 & $-$5.8 & $-$13.1 & $+$0.8 & & 67.7 \\ | |
| 18 | +Excluding BTC and ETH & 2514 & 59.0 & $+$34.4 & $+$24.1 & $-$4.4 & $-$13.7 & & $-$20.1 & \\ | |
| 19 | +Excluding ETH (BTC only) & 2514 & 53.8 & $+$35.7 & $+$25.0 & $-$5.3 & $-$13.7 & $-$1.3 & $-$19.8 & 91.7 \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_rolling_summary.tex
+10 −0
@@ -0,0 +1,10 @@ | ||
| 1 | +\begin{tabular}{@{}lrrrrrr@{}} | |
| 2 | +\toprule | |
| 3 | +Window & Windows & Mean & Min & (date) & Max & (date) \\ | |
| 4 | +\midrule | |
| 5 | +original (200 calendar days, levels, forward-filled) & 3451 & 67.1 & 57.2 & 2020-09-26 & 81.5 & 2018-02-06 \\ | |
| 6 | +200 trading days & 2315 & 61.9 & 50.5 & 2017-10-27 & 73.4 & 2025-09-24 \\ | |
| 7 | +250 trading days & 2265 & 60.9 & 49.8 & 2018-01-23 & 72.1 & 2025-12-26 \\ | |
| 8 | +500 trading days & 2015 & 58.3 & 48.5 & 2019-01-24 & 66.5 & 2026-03-06 \\ | |
| 9 | +\bottomrule | |
| 10 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_rv_descriptives.tex
+17 −0
@@ -0,0 +1,17 @@ | ||
| 1 | +\begin{tabular}{@{}llrrrrrrrrr@{}} | |
| 2 | +\toprule | |
| 3 | +Asset & Class & Mean & Median & Max & Skew & Skew & Kurt & $\rho_1$ & ADF & KPSS \\ | |
| 4 | + & & \multicolumn{3}{c}{annualized RV (\%)} & level & log & log & log & log & log \\ | |
| 5 | +\midrule | |
| 6 | +ES & Equity & 13.9 & 11.2 & 111 & 3.78 & 0.60 & 0.62 & 0.84 & -4.8$^{***}$ & 0.98$^{*}$ \\ | |
| 7 | +NQ & Equity & 17.9 & 15.1 & 112 & 2.85 & 0.38 & 0.26 & 0.83 & -5.2$^{***}$ & 1.45$^{*}$ \\ | |
| 8 | +EURUSD & FX & 7.0 & 6.5 & 32 & 2.03 & 0.41 & 0.45 & 0.68 & -4.8$^{***}$ & 0.23 \\ | |
| 9 | +USDJPY & FX & 7.7 & 6.9 & 35 & 1.94 & 0.28 & 0.17 & 0.74 & -5.2$^{***}$ & 0.97$^{*}$ \\ | |
| 10 | +GBPUSD & FX & 8.4 & 7.7 & 51 & 3.32 & 0.77 & 1.66 & 0.72 & -5.6$^{***}$ & 1.08$^{*}$ \\ | |
| 11 | +GC & Commodity & 13.6 & 12.1 & 91 & 3.84 & 0.83 & 1.75 & 0.72 & -4.4$^{***}$ & 1.75$^{*}$ \\ | |
| 12 | +CL & Commodity & 33.8 & 28.8 & 328 & 5.85 & 1.36 & 4.00 & 0.83 & -4.1$^{***}$ & 0.55$^{*}$ \\ | |
| 13 | +BTC & Crypto & 103.4 & 53.3 & 1409 & 3.90 & 1.02 & 0.90 & 0.91 & -3.4$^{**}$ & 2.51$^{*}$ \\ | |
| 14 | +ETH & Crypto & 113.2 & 79.3 & 1281 & 4.31 & 0.60 & 0.51 & 0.85 & -3.0$^{**}$ & 4.46$^{*}$ \\ | |
| 15 | +VIX & Volatility & 115.8 & 101.5 & 683 & 2.01 & 0.18 & 0.14 & 0.55 & -10.8$^{***}$ & 0.99$^{*}$ \\ | |
| 16 | +\bottomrule | |
| 17 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_sessions.tex
+21 −0
@@ -0,0 +1,21 @@ | ||
| 1 | +\begin{tabular}{@{}llrrrr@{}} | |
| 2 | +\toprule | |
| 3 | +Asset & Session (UTC) & Days & Mean $|r|$ (\%) & Annualized vol.\ (\%) & Share of day (\%) \\ | |
| 4 | +\midrule | |
| 5 | +ES & Asian 00:00--08:00 & 2583 & 0.024 & 5.1 & 16.2 \\ | |
| 6 | + & European 08:00--14:30 & 2581 & 0.037 & 7.3 & 30.8 \\ | |
| 7 | + & U.S. 14:30--21:00 & 2578 & 0.054 & 9.9 & 53.1 \\ | |
| 8 | +\addlinespace | |
| 9 | +NQ & Asian 00:00--08:00 & 2583 & 0.029 & 6.2 & 14.3 \\ | |
| 10 | + & European 08:00--14:30 & 2581 & 0.046 & 9.5 & 31.8 \\ | |
| 11 | + & U.S. 14:30--21:00 & 2578 & 0.069 & 12.8 & 54.0 \\ | |
| 12 | +\addlinespace | |
| 13 | +VIX & Asian 00:00--08:00 & 0 & 0.231 & -- & -- \\ | |
| 14 | + & European 08:00--14:30 & 2492 & 0.272 & 58.6 & 36.9 \\ | |
| 15 | + & U.S. 14:30--21:00 & 2518 & 0.444 & 80.6 & 63.5 \\ | |
| 16 | +\addlinespace | |
| 17 | +BTC & Asian 00:00--08:00 & 2610 & 0.255 & 56.9 & 36.6 \\ | |
| 18 | + & European 08:00--14:30 & 2609 & 0.260 & 51.2 & 25.3 \\ | |
| 19 | + & U.S. 14:30--21:00 & 2608 & 0.287 & 56.8 & 38.2 \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_sessions_predictive.tex
+17 −0
@@ -0,0 +1,17 @@ | ||
| 1 | +\begin{tabular}{@{}lrrrrr@{}} | |
| 2 | +\toprule | |
| 3 | +Predictive relation & $T$ & Coef.\ (same day) & Wald (HAC) & $p$ & $\Delta R^2$ \\ | |
| 4 | +\midrule | |
| 5 | +BTC Asian (t) $\rightarrow$ ES U.S. (t) & 2574 & $+$0.033 (0.019) & 6.65 & 0.155 & 0.001 \\ | |
| 6 | +BTC European (t) $\rightarrow$ ES U.S. (t) & 2574 & $+$0.040 (0.021) & 4.17 & 0.383 & 0.001 \\ | |
| 7 | +BTC Asian (t) $\rightarrow$ NQ U.S. (t) & 2574 & $+$0.024 (0.019) & 6.29 & 0.179 & 0.001 \\ | |
| 8 | +BTC European (t) $\rightarrow$ NQ U.S. (t) & 2574 & $+$0.036 (0.022) & 3.48 & 0.480 & 0.001 \\ | |
| 9 | +BTC Asian (t) $\rightarrow$ VIX U.S. (t) & 2514 & $+$0.058 (0.021) & 30.92$^{***}$ & 0.000 & 0.007 \\ | |
| 10 | +BTC European (t) $\rightarrow$ VIX U.S. (t) & 2514 & $+$0.056 (0.022) & 28.66$^{***}$ & 0.000 & 0.007 \\ | |
| 11 | +ES U.S. (t$-$1) $\rightarrow$ BTC Asian (t) & 2482 & $+$0.099 (0.021) & 27.70$^{***}$ & 0.000 & 0.003 \\ | |
| 12 | +NQ U.S. (t$-$1) $\rightarrow$ BTC Asian (t) & 2482 & $+$0.086 (0.022) & 20.52$^{***}$ & 0.000 & 0.002 \\ | |
| 13 | +VIX U.S. (t$-$1) $\rightarrow$ BTC Asian (t) & 2242 & $+$0.080 (0.022) & 17.35$^{***}$ & 0.002 & 0.002 \\ | |
| 14 | +ES Asian (t) $\rightarrow$ BTC U.S. (t) & 2492 & $+$0.093 (0.024) & 19.29$^{***}$ & 0.001 & 0.002 \\ | |
| 15 | +ES Asian (t) $\rightarrow$ ES U.S. (t) [own overnight] & 2570 & $+$0.382 (0.028) & 222.28$^{***}$ & 0.000 & 0.046 \\ | |
| 16 | +\bottomrule | |
| 17 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_weekend_btc.tex
+9 −0
@@ -0,0 +1,9 @@ | ||
| 1 | +\begin{tabular}{@{}lrrrrr@{}} | |
| 2 | +\toprule | |
| 3 | +Specification & $N$ & $\ln \mathrm{RV}^{\mathrm{ES}}_{\mathrm{Fri}}$ & $\ln \mathrm{RV}^{\mathrm{BTC}}_{\mathrm{weekend}}$ & $\ln \mathrm{RV}^{\mathrm{BTC}}_{\mathrm{Mon,\,Asian}}$ & $R^2$ \\ | |
| 4 | +\midrule | |
| 5 | +Friday controls only & 501 & $+$0.810 & -- & -- & 0.482 \\ | |
| 6 | ++ weekend BTC & 501 & $+$0.805 & $-$0.043 (0.052) & -- & 0.483 \\ | |
| 7 | ++ weekend BTC + Monday Asian BTC & 501 & $+$0.803 & $-$0.099 (0.061) & $+$0.094$^{*}$ & 0.486 \\ | |
| 8 | +\bottomrule | |
| 9 | +\end{tabular} | |
| \ No newline at end of file | ||
added
paper/tables/tab_yearly.tex
+17 −0
@@ -0,0 +1,17 @@ | ||
| 1 | +\begin{tabular}{@{}lrrrrrrr@{}} | |
| 2 | +\toprule | |
| 3 | +Year & $T$ & TSI & NET BTC & NET ETH & FROM BTC & BTC $\leftarrow$ ES & ES $\leftarrow$ BTC \\ | |
| 4 | + & & (\%) & (pp) & (pp) & excl.\ ETH (\%) & (\%) & (\%) \\ | |
| 5 | +\midrule | |
| 6 | +2016 & 200 & 55.4 {\scriptsize[55.1, 63.2]} & $+$25.4 {\scriptsize[$-$13.9, $+$51.0]} & $+$1.4 & 13.8 & 0.4 & 3.3 \\ | |
| 7 | +2017 & 251 & 51.0 {\scriptsize[51.1, 57.5]} & $-$3.9 {\scriptsize[$-$24.3, $+$12.0]} & $+$5.1 & 8.7 & 0.2 & 0.0 \\ | |
| 8 | +2018 & 251 & 51.7 {\scriptsize[50.7, 59.2]} & $+$18.0 {\scriptsize[$-$13.9, $+$44.6]} & $-$12.6 & 22.8 & 7.5 & 8.8 \\ | |
| 9 | +2019 & 252 & 54.4 {\scriptsize[52.5, 61.3]} & $+$11.3 {\scriptsize[$-$13.3, $+$22.3]} & $-$10.0 & 6.8 & 0.5 & 0.2 \\ | |
| 10 | +2020 & 253 & 61.5 {\scriptsize[57.7, 67.6]} & $-$13.2 {\scriptsize[$-$32.8, $+$11.0]} & $-$15.2 & 34.4 & 2.3 & 0.9 \\ | |
| 11 | +2021 & 252 & 60.6 {\scriptsize[57.6, 66.4]} & $-$14.6 {\scriptsize[$-$30.6, $+$0.1]} & $-$6.7 & 23.5 & 4.5 & 1.3 \\ | |
| 12 | +2022 & 254 & 61.2 {\scriptsize[59.9, 67.1]} & $-$1.6 {\scriptsize[$-$14.7, $+$12.9]} & $+$1.0 & 25.7 & 5.9 & 3.8 \\ | |
| 13 | +2023 & 250 & 62.6 {\scriptsize[59.3, 68.6]} & $-$11.5 {\scriptsize[$-$29.5, $+$5.7]} & $-$7.4 & 20.2 & 3.6 & 0.6 \\ | |
| 14 | +2024 & 252 & 62.1 {\scriptsize[59.5, 68.7]} & $-$7.7 {\scriptsize[$-$15.4, $+$4.5]} & $-$10.3 & 24.2 & 5.2 & 3.2 \\ | |
| 15 | +2025 & 251 & 71.5 {\scriptsize[67.9, 75.2]} & $-$3.2 {\scriptsize[$-$20.3, $+$18.5]} & $-$20.2 & 46.2 & 10.0 & 7.7 \\ | |
| 16 | +\bottomrule | |
| 17 | +\end{tabular} | |
| \ No newline at end of file | ||
added
results/rev_audit_construction.csv
+4 −0
@@ -0,0 +1,4 @@ | ||
| 1 | +Construction,T,TSI,NET_ES,NET_NQ,NET_VIX,NET_BTC,NET_USDJPY | |
| 2 | +"Original: calendar days, forward-filled, RV levels",3651,55.44,26.80,19.72,-23.37,1.23,-5.03 | |
| 3 | +"Trading days, RV levels",2514,50.04,41.61,29.84,-23.36,1.62,-8.01 | |
| 4 | +"Trading days, log RV (revised baseline)",2514,54.75,35.95,25.58,-20.55,1.72,-5.22 | |
added
results/rev_intraday_btc_dayofweek.csv
+8 −0
@@ -0,0 +1,8 @@ | ||
| 1 | +datetime,ann_vol_pct | |
| 2 | +0,106.02596236864791 | |
| 3 | +1,104.42831259466517 | |
| 4 | +2,104.15464896915618 | |
| 5 | +3,103.96634892250822 | |
| 6 | +4,103.8956132536647 | |
| 7 | +5,95.91904046063267 | |
| 8 | +6,98.72948187583829 | |
added
results/rev_intraday_hourly_absret_eastern.csv
+25 −0
@@ -0,0 +1,25 @@ | ||
| 1 | +hour_eastern,ES,NQ,VIX,BTC | |
| 2 | +0,0.01787,0.02160,,0.26199 | |
| 3 | +1,0.02170,0.02646,,0.25557 | |
| 4 | +2,0.02680,0.03233,,0.24389 | |
| 5 | +3,0.03705,0.04412,0.23089,0.24187 | |
| 6 | +4,0.03223,0.03873,0.21345,0.24596 | |
| 7 | +5,0.02810,0.03345,0.18800,0.24571 | |
| 8 | +6,0.02797,0.03343,0.18815,0.25074 | |
| 9 | +7,0.03008,0.03688,0.21338,0.25903 | |
| 10 | +8,0.03876,0.04795,0.31638,0.26863 | |
| 11 | +9,0.05964,0.08573,0.55840,0.26583 | |
| 12 | +10,0.06878,0.09525,0.55529,0.26787 | |
| 13 | +11,0.05588,0.07442,0.45274,0.27376 | |
| 14 | +12,0.04775,0.06231,0.38427,0.28195 | |
| 15 | +13,0.04811,0.06121,0.38158,0.28409 | |
| 16 | +14,0.05323,0.06585,0.41556,0.29005 | |
| 17 | +15,0.06381,0.07470,0.47658,0.28201 | |
| 18 | +16,0.03005,0.03808,0.36511,0.27891 | |
| 19 | +17,0.00491,0.00616,,0.25823 | |
| 20 | +18,0.02487,0.02976,,0.25430 | |
| 21 | +19,0.02349,0.02757,,0.24967 | |
| 22 | +20,0.02759,0.03324,,0.25226 | |
| 23 | +21,0.02599,0.03136,,0.25109 | |
| 24 | +22,0.02125,0.02588,,0.24996 | |
| 25 | +23,0.01808,0.02180,,0.24884 | |
added
results/rev_intraday_hourly_absret_utc.csv
+25 −0
@@ -0,0 +1,25 @@ | ||
| 1 | +hour_utc,ES,NQ,VIX,BTC | |
| 2 | +0,0.02729,0.03226,,0.25076 | |
| 3 | +1,0.02768,0.03352,,0.25286 | |
| 4 | +2,0.02217,0.02687,,0.24838 | |
| 5 | +3,0.01920,0.02334,,0.25050 | |
| 6 | +4,0.01688,0.02036,,0.25799 | |
| 7 | +5,0.02139,0.02598,,0.25906 | |
| 8 | +6,0.02467,0.02969,,0.24970 | |
| 9 | +7,0.03366,0.04024,0.23076,0.24011 | |
| 10 | +8,0.03420,0.04093,0.21999,0.24769 | |
| 11 | +9,0.02935,0.03514,0.19611,0.24395 | |
| 12 | +10,0.02773,0.03333,0.18636,0.24876 | |
| 13 | +11,0.02928,0.03546,0.20430,0.25349 | |
| 14 | +12,0.03585,0.04407,0.28661,0.26394 | |
| 15 | +13,0.05235,0.07241,0.45141,0.26614 | |
| 16 | +14,0.06528,0.09186,0.55405,0.26984 | |
| 17 | +15,0.06089,0.08233,0.49124,0.26834 | |
| 18 | +16,0.05045,0.06653,0.40683,0.28211 | |
| 19 | +17,0.04788,0.06136,0.38571,0.28320 | |
| 20 | +18,0.05170,0.06451,0.40446,0.28705 | |
| 21 | +19,0.06020,0.07165,0.45383,0.28274 | |
| 22 | +20,0.04264,0.05186,0.44470,0.28107 | |
| 23 | +21,0.02900,0.03723,0.36454,0.26898 | |
| 24 | +22,0.02423,0.02876,,0.25730 | |
| 25 | +23,0.02329,0.02767,,0.24828 | |
added
results/rev_intraday_key_numbers.csv
+29 −0
@@ -0,0 +1,29 @@ | ||
| 1 | +,value | |
| 2 | +btc_weekend_share_pct,22.05080097534448 | |
| 3 | +ES_peak_hour_utc,14.0 | |
| 4 | +ES_peak_absret,0.06527739578754627 | |
| 5 | +ES_min_hour_utc,4.0 | |
| 6 | +ES_min_absret,0.016883222968725735 | |
| 7 | +ES_peak_to_trough,3.8664060711906294 | |
| 8 | +NQ_peak_hour_utc,14.0 | |
| 9 | +NQ_peak_absret,0.09185518484491462 | |
| 10 | +NQ_min_hour_utc,4.0 | |
| 11 | +NQ_min_absret,0.0203589380590271 | |
| 12 | +NQ_peak_to_trough,4.5117866451873345 | |
| 13 | +VIX_peak_hour_utc,14.0 | |
| 14 | +VIX_peak_absret,0.5540546012159561 | |
| 15 | +VIX_min_hour_utc,10.0 | |
| 16 | +VIX_min_absret,0.18636498080192462 | |
| 17 | +VIX_peak_to_trough,2.972954461894454 | |
| 18 | +BTC_peak_hour_utc,18.0 | |
| 19 | +BTC_peak_absret,0.2870529938044476 | |
| 20 | +BTC_min_hour_utc,7.0 | |
| 21 | +BTC_min_absret,0.2401057997612897 | |
| 22 | +BTC_peak_to_trough,1.195527113838284 | |
| 23 | +BTC_dow0_annvol,106.02596236864791 | |
| 24 | +BTC_dow1_annvol,104.42831259466517 | |
| 25 | +BTC_dow2_annvol,104.15464896915618 | |
| 26 | +BTC_dow3_annvol,103.96634892250822 | |
| 27 | +BTC_dow4_annvol,103.8956132536647 | |
| 28 | +BTC_dow5_annvol,95.91904046063267 | |
| 29 | +BTC_dow6_annvol,98.72948187583829 | |
added
results/rev_intraday_session_predictive.csv
+12 −0
@@ -0,0 +1,12 @@ | ||
| 1 | +Test,T,coef_x_l0,se_x_l0,Wald_HAC,p,R2_with,R2_without | |
| 2 | +BTC Asian (t) $\rightarrow$ ES U.S. (t),2574,0.0331,0.0189,6.6539,0.1553,0.5482,0.5471 | |
| 3 | +BTC European (t) $\rightarrow$ ES U.S. (t),2574,0.0405,0.0212,4.1739,0.3830,0.5479,0.5471 | |
| 4 | +BTC Asian (t) $\rightarrow$ NQ U.S. (t),2574,0.0245,0.0192,6.2875,0.1787,0.5221,0.5210 | |
| 5 | +BTC European (t) $\rightarrow$ NQ U.S. (t),2574,0.0360,0.0216,3.4841,0.4803,0.5217,0.5210 | |
| 6 | +BTC Asian (t) $\rightarrow$ VIX U.S. (t),2514,0.0581,0.0212,30.9211,0.0000,0.3708,0.3640 | |
| 7 | +BTC European (t) $\rightarrow$ VIX U.S. (t),2514,0.0562,0.0216,28.6555,0.0000,0.3706,0.3640 | |
| 8 | +ES U.S. (t$-$1) $\rightarrow$ BTC Asian (t),2482,0.0988,0.0211,27.6999,0.0000,0.7767,0.7741 | |
| 9 | +NQ U.S. (t$-$1) $\rightarrow$ BTC Asian (t),2482,0.0855,0.0215,20.5243,0.0004,0.7760,0.7741 | |
| 10 | +VIX U.S. (t$-$1) $\rightarrow$ BTC Asian (t),2242,0.0801,0.0219,17.3543,0.0016,0.7747,0.7730 | |
| 11 | +ES Asian (t) $\rightarrow$ BTC U.S. (t),2492,0.0929,0.0245,19.2918,0.0007,0.7774,0.7759 | |
| 12 | +ES Asian (t) $\rightarrow$ ES U.S. (t) [own overnight],2570,0.3816,0.0277,222.2827,0.0000,0.5845,0.5385 | |
added
results/rev_intraday_sessions.csv
+13 −0
@@ -0,0 +1,13 @@ | ||
| 1 | +Asset,Session,Days,Ann_vol_pct,Mean_absret_pct,Share_of_day_pct | |
| 2 | +ES,Asian,2583,5.1462,0.0241,16.2488 | |
| 3 | +ES,European,2581,7.3291,0.0367,30.7559 | |
| 4 | +ES,US,2578,9.8750,0.0539,53.1219 | |
| 5 | +NQ,Asian,2583,6.1904,0.0290,14.2805 | |
| 6 | +NQ,European,2581,9.5290,0.0465,31.8458 | |
| 7 | +NQ,US,2578,12.8093,0.0695,54.0029 | |
| 8 | +VIX,Asian,0,,0.2308, | |
| 9 | +VIX,European,2492,58.6344,0.2723,36.9462 | |
| 10 | +VIX,US,2518,80.6120,0.4436,63.4750 | |
| 11 | +BTC,Asian,2610,56.9067,0.2555,36.5663 | |
| 12 | +BTC,European,2609,51.1559,0.2599,25.2933 | |
| 13 | +BTC,US,2608,56.8053,0.2867,38.1793 | |
added
results/rev_intraday_weekend_btc_monday_es.csv
+4 −0
@@ -0,0 +1,4 @@ | ||
| 1 | +model,N,coef_btc_wk,se_btc_wk,p_btc_wk,coef_btc_mon_asia,p_btc_mon_asia,coef_es_fri,R2 | |
| 2 | +Friday controls only,501,,,,,,0.8096,0.4824 | |
| 3 | ++ weekend BTC,501,-0.0433,0.0524,0.4088,,,0.8051,0.4831 | |
| 4 | ++ weekend BTC + Monday Asian BTC,501,-0.0988,0.0614,0.1074,0.0943,0.0998,0.8027,0.4855 | |
added
results/rev_key_numbers.csv
+111 −0
@@ -0,0 +1,111 @@ | ||
| 1 | +,value | |
| 2 | +T_panel,2514 | |
| 3 | +T_original_panel,3651 | |
| 4 | +weekend_rows_original,1044 | |
| 5 | +ffilled_rows_original,1137 | |
| 6 | +TSI,54.75166394316902 | |
| 7 | +TSI_lo,53.14641120369146 | |
| 8 | +TSI_hi,56.89074660976463 | |
| 9 | +TSI_original_replicated,55.44044705719146 | |
| 10 | +TSI_levels_trading_days,50.04220348751443 | |
| 11 | +NET_ES,35.949117657126024 | |
| 12 | +NET_ES_lo,29.8532195028492 | |
| 13 | +NET_ES_hi,41.540053420913736 | |
| 14 | +TO_ES,104.08527814650698 | |
| 15 | +FROM_ES,68.13616048938096 | |
| 16 | +OWN_ES,31.863839510619048 | |
| 17 | +NET_NQ,25.5828743465963 | |
| 18 | +NET_NQ_lo,19.041782709243893 | |
| 19 | +NET_NQ_hi,31.271595755762227 | |
| 20 | +TO_NQ,91.89518796369128 | |
| 21 | +FROM_NQ,66.31231361709499 | |
| 22 | +OWN_NQ,33.68768638290503 | |
| 23 | +NET_EURUSD,-0.3856168034419909 | |
| 24 | +NET_EURUSD_lo,-6.016249823751177 | |
| 25 | +NET_EURUSD_hi,5.803045119763542 | |
| 26 | +TO_EURUSD,64.13837618771167 | |
| 27 | +FROM_EURUSD,64.52399299115366 | |
| 28 | +OWN_EURUSD,35.47600700884633 | |
| 29 | +NET_USDJPY,-5.220511142313001 | |
| 30 | +NET_USDJPY_lo,-10.170678731690995 | |
| 31 | +NET_USDJPY_hi,0.17174483503590832 | |
| 32 | +TO_USDJPY,50.23942223555866 | |
| 33 | +FROM_USDJPY,55.459933377871664 | |
| 34 | +OWN_USDJPY,44.54006662212836 | |
| 35 | +NET_GBPUSD,-13.244483743905505 | |
| 36 | +NET_GBPUSD_lo,-17.998455803803783 | |
| 37 | +NET_GBPUSD_hi,-7.446918804451237 | |
| 38 | +TO_GBPUSD,46.6412142303967 | |
| 39 | +FROM_GBPUSD,59.885697974302204 | |
| 40 | +OWN_GBPUSD,40.11430202569779 | |
| 41 | +NET_GC,-7.227262753807516 | |
| 42 | +NET_GC_lo,-12.499070319861985 | |
| 43 | +NET_GC_hi,-0.7904042708884056 | |
| 44 | +TO_GC,51.41338438033329 | |
| 45 | +FROM_GC,58.640647134140806 | |
| 46 | +OWN_GC,41.359352865859194 | |
| 47 | +NET_CL,-14.233290631844895 | |
| 48 | +NET_CL_lo,-21.57058830865831 | |
| 49 | +NET_CL_hi,-6.654728928239155 | |
| 50 | +TO_CL,31.824511510171874 | |
| 51 | +FROM_CL,46.05780214201677 | |
| 52 | +OWN_CL,53.942197857983246 | |
| 53 | +NET_BTC,1.7246867252108231 | |
| 54 | +NET_BTC_lo,-3.34699558961494 | |
| 55 | +NET_BTC_hi,6.3526856689929225 | |
| 56 | +TO_BTC,35.05019494860863 | |
| 57 | +FROM_BTC,33.325508223397804 | |
| 58 | +OWN_BTC,66.67449177660218 | |
| 59 | +NET_ETH,-2.3924430435704878 | |
| 60 | +NET_ETH_lo,-7.946215928470087 | |
| 61 | +NET_ETH_hi,2.1320008836845985 | |
| 62 | +TO_ETH,32.683774104014965 | |
| 63 | +FROM_ETH,35.07621714758545 | |
| 64 | +OWN_ETH,64.92378285241453 | |
| 65 | +NET_VIX,-20.55307061004975 | |
| 66 | +NET_VIX_lo,-25.212536248688842 | |
| 67 | +NET_VIX_hi,-13.95741532552259 | |
| 68 | +TO_VIX,39.545295724696274 | |
| 69 | +FROM_VIX,60.098366334746025 | |
| 70 | +OWN_VIX,39.901633665253975 | |
| 71 | +BTC_ETH,27.047475173306566 | |
| 72 | +ETH_BTC,27.94727906979007 | |
| 73 | +VIX_from_ES,21.233234622500756 | |
| 74 | +VIX_from_NQ,18.45133457568511 | |
| 75 | +BTC_from_traditional,6.2780330500912385 | |
| 76 | +ETH_from_traditional,7.128938077795382 | |
| 77 | +roll200_mean,61.89545321102092 | |
| 78 | +roll200_min,50.54260391999175 | |
| 79 | +roll200_max,73.37407735058166 | |
| 80 | +roll200_min_date,2017-10-27 | |
| 81 | +roll200_max_date,2025-09-24 | |
| 82 | +roll200_last_NET_BTC,-14.888762832948487 | |
| 83 | +roll200_last_NET_ES,17.977012416725643 | |
| 84 | +roll200_NET_BTC_2025_mean,-6.622970515639605 | |
| 85 | +roll200_NET_BTC_2017_mean,-1.2065582034350346 | |
| 86 | +roll200_share_BTC_positive,0.3434125269978402 | |
| 87 | +roll250_mean,60.911807123874105 | |
| 88 | +roll250_min,49.7971156186276 | |
| 89 | +roll250_max,72.08112365846111 | |
| 90 | +roll250_min_date,2018-01-23 | |
| 91 | +roll250_max_date,2025-12-26 | |
| 92 | +roll250_last_NET_BTC,-12.107619321242268 | |
| 93 | +roll250_last_NET_ES,28.390902815984347 | |
| 94 | +roll250_NET_BTC_2025_mean,-8.46300190331161 | |
| 95 | +roll250_NET_BTC_2017_mean,-7.165505710331391 | |
| 96 | +roll250_share_BTC_positive,0.282560706401766 | |
| 97 | +roll500_mean,58.32826935432884 | |
| 98 | +roll500_min,48.529043411313246 | |
| 99 | +roll500_max,66.51910110906907 | |
| 100 | +roll500_min_date,2019-01-24 | |
| 101 | +roll500_max_date,2026-03-06 | |
| 102 | +roll500_last_NET_BTC,-19.12812368161417 | |
| 103 | +roll500_last_NET_ES,32.95039979328489 | |
| 104 | +roll500_NET_BTC_2025_mean,-7.766775742898419 | |
| 105 | +roll500_NET_BTC_2017_mean, | |
| 106 | +roll500_share_BTC_positive,0.2699751861042184 | |
| 107 | +roll200_2018-02-02,54.437744013510816 | |
| 108 | +roll200_2018-02-06,56.378983244042715 | |
| 109 | +roll200_2020-02-20,60.42762776576264 | |
| 110 | +roll200_2020-03-31,69.12944915540427 | |
| 111 | +roll200_2020-06-30,66.41597122865366 | |
added
results/rev_rolling_summary.csv
+5 −0
@@ -0,0 +1,5 @@ | ||
| 1 | +window,n_windows,mean,min,min_date,max,max_date | |
| 2 | +"original (200 calendar days, levels, forward-filled)",3451,67.13,57.22,2020-09-26,81.55,2018-02-06 | |
| 3 | +200 trading days,2315,61.90,50.54,2017-10-27,73.37,2025-09-24 | |
| 4 | +250 trading days,2265,60.91,49.80,2018-01-23,72.08,2025-12-26 | |
| 5 | +500 trading days,2015,58.33,48.53,2019-01-24,66.52,2026-03-06 | |
added
results/rev_rolling_w200.csv
+2316 −0
@@ -0,0 +1,2316 @@ | ||
| 1 | +date,TSI,NET_ES,NET_NQ,NET_EURUSD,NET_USDJPY,NET_GBPUSD,NET_GC,NET_CL,NET_BTC,NET_ETH,NET_VIX | |
| 2 | +2016-12-30,57.887,23.508,11.702,-9.373,-1.991,-19.351,-14.646,-2.385,14.337,0.769,-2.571 | |
| 3 | +2017-01-03,58.778,22.884,11.962,-10.825,-1.433,-19.344,-16.464,-3.285,18.476,-0.011,-1.960 | |
| 4 | +2017-01-04,59.122,22.575,12.170,-12.947,-2.374,-19.979,-17.435,-4.173,21.619,3.573,-3.030 | |
| 5 | +2017-01-05,59.900,20.967,10.263,-15.883,-6.410,-22.102,-18.496,-5.737,23.310,18.653,-4.564 | |
| 6 | +2017-01-06,59.484,21.727,11.953,-14.616,-6.424,-20.501,-16.737,-4.666,18.180,14.502,-3.417 | |
| 7 | +2017-01-09,58.737,25.600,16.079,-13.835,-4.745,-19.495,-14.934,1.714,9.702,1.714,-1.800 | |
| 8 | +2017-01-10,58.555,26.599,17.026,-13.524,-4.411,-19.132,-13.624,1.573,8.113,-1.160,-1.460 | |
| 9 | +2017-01-11,59.087,26.370,16.064,-13.724,-6.240,-19.345,-15.455,1.611,10.621,2.103,-2.006 | |
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| 1768 | +2024-01-04,56.694,5.318,-0.541,-2.403,0.799,-4.851,6.437,-4.558,0.753,13.166,-14.121 | |
| 1769 | +2024-01-05,56.947,5.384,-1.765,-1.166,-0.192,-3.053,6.233,-5.447,1.454,13.551,-14.998 | |
| 1770 | +2024-01-08,57.093,6.744,-1.147,-0.350,-1.744,-3.344,6.307,-8.444,1.957,12.969,-12.948 | |
| 1771 | +2024-01-09,57.046,6.996,-1.691,0.318,-1.990,-2.463,6.358,-7.857,1.361,12.224,-13.257 | |
| 1772 | +2024-01-10,56.976,6.503,-1.941,0.570,-2.010,-2.341,6.074,-8.241,1.759,12.489,-12.862 | |
| 1773 | +2024-01-11,57.110,8.281,-0.622,1.708,-2.763,-1.726,6.709,-8.989,0.532,10.521,-13.651 | |
| 1774 | +2024-01-12,56.986,7.753,-1.312,1.160,-2.737,-1.967,5.541,-8.591,1.771,12.234,-13.852 | |
| 1775 | +2024-01-16,56.576,9.457,0.616,1.235,-2.664,-1.699,4.744,-8.601,-1.378,7.256,-8.967 | |
| 1776 | +2024-01-17,56.459,9.784,1.162,1.513,-3.208,-1.564,4.767,-7.988,-2.057,6.126,-8.534 | |
| 1777 | +2024-01-18,56.500,9.828,1.539,1.476,-3.304,-1.134,6.302,-7.618,-3.446,5.845,-9.489 | |
| 1778 | +2024-01-19,56.601,9.585,1.583,1.570,-3.255,-0.720,6.731,-7.336,-3.812,5.248,-9.593 | |
| 1779 | +2024-01-22,56.543,10.012,1.527,2.109,-3.387,-0.524,6.813,-8.118,-4.040,5.242,-9.633 | |
| 1780 | +2024-01-23,56.527,11.872,0.274,2.018,-6.070,-0.001,4.923,-8.109,-3.787,7.123,-8.243 | |
| 1781 | +2024-01-24,56.454,11.202,0.293,1.905,-6.081,0.168,5.710,-8.453,-2.780,6.974,-8.938 | |
| 1782 | +2024-01-25,56.393,11.417,1.291,1.668,-3.884,-0.325,3.109,-5.002,-2.107,4.806,-10.974 | |
| 1783 | +2024-01-26,56.444,10.342,0.798,1.730,-3.132,-0.348,4.343,-5.248,-2.768,5.583,-11.299 | |
| 1784 | +2024-01-29,56.419,10.392,1.043,1.205,-1.909,-1.089,5.304,-5.553,-3.732,5.605,-11.265 | |
| 1785 | +2024-01-30,56.698,11.739,1.392,2.328,-4.275,-0.274,4.636,-6.201,-3.348,5.155,-11.151 | |
| 1786 | +2024-01-31,57.053,11.748,1.837,2.290,-4.479,0.155,3.108,-5.365,-3.270,5.268,-11.292 | |
| 1787 | +2024-02-01,56.935,10.964,1.838,1.351,-5.137,-1.190,1.405,-0.902,-2.498,5.136,-10.968 | |
| 1788 | +2024-02-02,57.022,11.309,1.667,1.121,-6.250,-1.117,3.316,-1.270,-3.032,5.402,-11.147 | |
| 1789 | +2024-02-05,57.221,11.831,2.105,1.523,-6.631,-0.783,4.364,-2.757,-3.240,6.237,-12.649 | |
| 1790 | +2024-02-06,57.429,11.915,1.363,1.359,-7.594,-0.142,4.375,-1.611,-3.039,5.776,-12.403 | |
| 1791 | +2024-02-07,57.643,12.547,1.027,2.105,-7.651,0.424,4.192,-1.187,-3.985,3.915,-11.387 | |
| 1792 | +2024-02-08,57.881,12.896,2.552,1.203,-8.102,0.377,3.122,-0.020,-4.061,2.707,-10.675 | |
| 1793 | +2024-02-09,57.850,12.757,3.001,0.463,-6.487,-0.331,1.783,0.398,-4.478,1.935,-9.040 | |
| 1794 | +2024-02-12,57.904,9.462,2.465,-0.746,-0.185,-0.138,1.677,1.156,-4.502,3.038,-12.226 | |
| 1795 | +2024-02-13,58.180,10.511,4.518,0.121,-1.146,2.445,-3.790,2.204,-5.332,2.708,-12.239 | |
| 1796 | +2024-02-14,57.881,9.013,4.029,0.773,-1.372,1.775,-1.496,1.906,-3.490,3.393,-14.531 | |
| 1797 | +2024-02-15,58.009,10.105,3.962,1.922,-3.372,0.995,-2.162,0.044,-3.056,4.495,-12.935 | |
| 1798 | +2024-02-16,57.703,9.174,2.833,3.021,-2.838,0.967,-1.092,0.685,-3.759,3.776,-12.768 | |
| 1799 | +2024-02-20,57.459,9.593,2.969,4.498,-2.698,0.947,-1.676,1.111,-5.347,2.599,-11.997 | |
| 1800 | +2024-02-21,57.190,9.341,2.484,3.958,-2.589,0.545,-0.690,1.182,-4.787,2.954,-12.399 | |
| 1801 | +2024-02-22,57.148,9.056,1.948,3.748,-2.233,0.565,0.170,1.226,-4.858,2.551,-12.173 | |
| 1802 | +2024-02-23,57.256,9.856,2.288,3.874,-3.148,1.294,-1.268,0.453,-4.841,3.511,-12.017 | |
| 1803 | +2024-02-26,57.455,10.117,2.039,5.418,-3.458,1.740,-2.021,0.489,-5.192,4.130,-13.264 | |
| 1804 | +2024-02-27,58.069,11.622,2.500,8.468,-5.135,2.294,-0.961,0.257,-7.100,2.842,-14.787 | |
| 1805 | +2024-02-28,58.470,12.516,3.422,10.400,-5.796,2.728,-0.938,0.111,-9.272,0.477,-13.649 | |
| 1806 | +2024-02-29,58.601,13.238,4.542,10.270,-5.670,2.982,-1.920,-0.298,-9.971,0.049,-13.222 | |
| 1807 | +2024-03-01,58.740,13.400,5.243,11.995,-6.479,3.981,-3.356,-1.789,-9.840,-1.005,-12.150 | |
| 1808 | +2024-03-04,59.252,14.065,6.466,14.266,-6.595,5.783,-4.452,-2.832,-11.184,-3.862,-11.654 | |
| 1809 | +2024-03-05,59.407,14.737,7.765,15.185,-4.567,7.804,-3.743,-4.088,-14.075,-8.333,-10.686 | |
| 1810 | +2024-03-06,59.459,13.694,7.561,17.961,-4.546,9.933,-4.259,-4.334,-14.565,-8.544,-12.900 | |
| 1811 | +2024-03-07,59.299,13.842,7.605,15.917,-6.719,7.307,-3.986,-2.559,-11.693,-6.875,-12.839 | |
| 1812 | +2024-03-08,59.335,12.890,7.229,16.965,-3.266,9.211,-4.133,-3.229,-14.256,-9.602,-11.810 | |
| 1813 | +2024-03-11,58.887,12.728,6.906,17.200,-5.358,8.531,-8.376,-0.823,-13.204,-8.729,-8.874 | |
| 1814 | +2024-03-12,59.010,12.926,6.912,19.465,-6.129,10.442,-10.566,-1.411,-13.817,-9.009,-8.813 | |
| 1815 | +2024-03-13,59.234,12.850,7.273,19.287,-7.081,9.256,-10.261,-1.608,-12.718,-7.662,-9.335 | |
| 1816 | +2024-03-14,59.314,11.767,6.789,20.190,-6.409,9.843,-11.008,-1.172,-13.568,-8.390,-8.042 | |
| 1817 | +2024-03-15,59.685,11.005,5.886,23.945,-5.657,12.426,-11.815,-0.930,-16.481,-11.402,-6.976 | |
| 1818 | +2024-03-18,59.438,10.701,6.075,23.335,-5.862,11.422,-11.894,-0.837,-15.289,-9.842,-7.810 | |
| 1819 | +2024-03-19,59.942,9.987,4.935,27.728,-6.768,14.646,-12.213,-1.524,-17.051,-11.271,-8.469 | |
| 1820 | +2024-03-20,60.397,11.094,6.260,29.103,-5.241,17.059,-10.223,-6.595,-18.205,-14.064,-9.187 | |
| 1821 | +2024-03-21,60.061,11.799,6.627,27.088,-7.850,14.929,-11.218,-4.212,-16.564,-12.648,-7.952 | |
| 1822 | +2024-03-22,60.622,12.101,7.776,29.621,-6.743,16.417,-11.634,-7.056,-17.933,-13.961,-8.589 | |
| 1823 | +2024-03-25,60.229,11.061,6.764,28.298,-6.452,15.828,-12.409,-5.862,-15.993,-12.785,-8.450 | |
| 1824 | +2024-03-26,60.153,11.134,7.435,28.703,-6.085,15.741,-13.273,-7.255,-15.580,-12.240,-8.581 | |
| 1825 | +2024-03-27,60.252,11.238,8.112,30.793,-5.280,16.614,-14.299,-6.575,-17.578,-14.173,-8.851 | |
| 1826 | +2024-03-28,60.074,10.934,7.454,31.310,-4.653,16.254,-15.866,-7.352,-15.523,-12.378,-10.180 | |
| 1827 | +2024-04-01,59.861,8.886,4.589,29.930,-3.650,15.435,-15.414,-9.001,-12.145,-7.981,-10.649 | |
| 1828 | +2024-04-02,60.195,8.501,5.687,29.835,-1.155,17.173,-15.680,-8.202,-15.453,-10.199,-10.508 | |
| 1829 | +2024-04-03,59.851,7.562,4.258,30.009,-0.242,16.389,-16.863,-6.970,-13.544,-9.041,-11.557 | |
| 1830 | +2024-04-04,60.028,8.036,5.207,29.869,1.074,15.391,-16.762,-9.737,-13.827,-8.183,-11.068 | |
| 1831 | +2024-04-05,59.953,7.983,4.242,29.346,0.943,14.054,-17.089,-9.668,-11.710,-6.978,-11.124 | |
| 1832 | +2024-04-08,60.037,9.187,6.489,29.124,1.446,13.645,-17.373,-12.066,-13.495,-8.149,-8.808 | |
| 1833 | +2024-04-09,60.378,9.027,6.170,28.906,2.696,13.301,-17.034,-14.270,-13.355,-7.762,-7.680 | |
| 1834 | +2024-04-10,61.189,11.247,8.963,26.556,3.419,13.620,-16.882,-14.379,-14.368,-8.913,-9.263 | |
| 1835 | +2024-04-11,61.160,11.246,8.330,25.318,1.812,14.079,-16.364,-11.985,-13.495,-7.888,-11.051 | |
| 1836 | +2024-04-12,61.417,11.794,7.988,25.937,2.961,14.697,-14.935,-12.574,-14.137,-7.993,-13.739 | |
| 1837 | +2024-04-15,62.021,11.953,7.394,28.487,5.616,14.993,-11.943,-13.151,-15.672,-10.099,-17.576 | |
| 1838 | +2024-04-16,61.524,12.999,6.594,26.944,3.263,12.740,-8.605,-14.261,-13.759,-9.287,-16.627 | |
| 1839 | +2024-04-17,61.678,13.491,7.273,27.026,4.450,13.087,-10.587,-14.726,-13.610,-9.269,-17.135 | |
| 1840 | +2024-04-18,61.678,12.932,6.313,28.428,6.012,11.707,-8.580,-16.696,-13.542,-9.466,-17.108 | |
| 1841 | +2024-04-19,61.521,12.107,5.699,27.506,5.180,12.588,-9.772,-17.146,-12.795,-8.565,-14.801 | |
| 1842 | +2024-04-22,61.444,12.002,5.715,27.459,5.310,12.821,-11.138,-16.419,-12.634,-8.204,-14.912 | |
| 1843 | +2024-04-23,61.556,11.716,5.626,27.724,1.860,13.562,-10.786,-17.806,-10.589,-4.512,-16.796 | |
| 1844 | +2024-04-24,61.572,11.923,5.993,28.055,1.030,14.103,-9.485,-18.058,-11.157,-5.257,-17.146 | |
| 1845 | +2024-04-25,61.358,13.650,8.335,27.555,0.902,14.203,-9.588,-15.652,-13.027,-6.627,-19.750 | |
| 1846 | +2024-04-26,60.821,14.397,8.546,27.941,-0.722,14.754,-9.694,-14.903,-14.244,-9.084,-16.991 | |
| 1847 | +2024-04-29,60.331,13.111,7.402,27.024,1.847,13.745,-10.190,-13.276,-14.557,-9.462,-15.646 | |
| 1848 | +2024-04-30,60.419,14.032,7.838,27.636,-3.159,14.736,-8.926,-14.960,-13.560,-8.548,-15.089 | |
| 1849 | +2024-05-01,61.078,14.439,9.025,27.188,-1.488,14.550,-8.954,-17.070,-13.287,-7.841,-16.560 | |
| 1850 | +2024-05-02,60.550,13.568,6.120,26.109,-2.550,13.422,-8.574,-17.417,-10.073,-5.988,-14.617 | |
| 1851 | +2024-05-03,60.607,15.028,6.872,26.664,-5.291,13.377,-6.063,-18.024,-10.715,-7.019,-14.830 | |
| 1852 | +2024-05-06,60.540,14.076,5.688,26.321,-4.278,13.715,-5.883,-17.369,-11.023,-6.798,-14.448 | |
| 1853 | +2024-05-07,60.433,14.618,7.063,24.110,-4.440,14.358,-8.208,-17.658,-9.483,-5.518,-14.842 | |
| 1854 | +2024-05-08,61.013,15.220,8.861,23.804,-6.006,14.941,-8.609,-16.782,-9.609,-6.491,-15.329 | |
| 1855 | +2024-05-09,60.853,14.229,6.694,24.209,-3.483,12.118,-9.112,-18.058,-6.600,-3.649,-16.350 | |
| 1856 | +2024-05-10,61.152,13.418,5.494,26.556,-2.744,12.332,-9.428,-18.097,-7.190,-3.533,-16.810 | |
| 1857 | +2024-05-13,61.035,12.784,4.598,23.877,-0.032,11.482,-10.672,-17.563,-5.494,-1.196,-17.783 | |
| 1858 | +2024-05-14,60.536,12.688,4.036,22.418,-0.614,11.446,-10.128,-17.487,-4.055,0.540,-18.842 | |
| 1859 | +2024-05-15,60.936,13.000,4.146,22.248,-0.400,12.078,-9.721,-20.119,-3.539,0.982,-18.674 | |
| 1860 | +2024-05-16,60.959,13.768,6.336,23.343,-3.208,12.431,-9.953,-20.765,-4.767,-1.685,-15.501 | |
| 1861 | +2024-05-17,61.339,15.135,8.260,24.322,-6.229,12.636,-12.013,-17.988,-6.333,-3.279,-14.511 | |
| 1862 | +2024-05-20,61.357,15.499,9.120,26.430,-6.071,14.550,-12.864,-16.930,-9.032,-5.604,-15.098 | |
| 1863 | +2024-05-21,61.116,15.291,9.326,25.881,-5.175,14.250,-13.176,-15.965,-7.480,-6.672,-16.281 | |
| 1864 | +2024-05-22,60.764,14.119,6.919,25.254,-4.635,13.893,-13.151,-15.232,-4.560,-5.695,-16.913 | |
| 1865 | +2024-05-23,60.884,14.036,7.061,24.160,-4.595,13.340,-13.601,-13.953,-4.349,-5.715,-16.384 | |
| 1866 | +2024-05-24,61.081,14.058,5.983,25.040,-4.637,13.198,-11.892,-15.410,-3.371,-5.538,-17.431 | |
| 1867 | +2024-05-28,61.223,13.777,5.296,25.765,-5.130,13.215,-11.260,-16.343,-2.830,-4.911,-17.579 | |
| 1868 | +2024-05-29,61.285,14.205,5.937,25.793,-4.663,14.801,-10.868,-16.711,-3.204,-9.197,-16.092 | |
| 1869 | +2024-05-30,60.832,13.893,5.794,24.459,-3.283,13.555,-11.200,-16.525,-2.158,-8.769,-15.766 | |
| 1870 | +2024-05-31,60.718,13.268,5.508,23.176,-3.728,12.789,-12.624,-16.230,-0.833,-6.450,-14.877 | |
| 1871 | +2024-06-03,60.378,13.172,5.479,22.425,-2.343,11.462,-12.457,-15.403,-0.626,-6.360,-15.350 | |
| 1872 | +2024-06-04,59.743,11.819,2.957,20.658,-1.884,7.874,-10.759,-16.115,2.556,-1.701,-15.406 | |
| 1873 | +2024-06-05,59.863,12.516,3.565,21.309,-2.039,7.615,-9.677,-17.999,2.820,-0.918,-17.192 | |
| 1874 | +2024-06-06,59.754,12.533,3.316,20.421,-1.966,5.963,-9.233,-17.817,3.435,0.867,-17.520 | |
| 1875 | +2024-06-07,59.895,13.209,3.495,20.311,-1.680,6.452,-8.708,-18.775,2.971,0.056,-17.332 | |
| 1876 | +2024-06-10,59.949,12.379,2.606,21.185,-2.897,6.164,-9.128,-18.086,5.002,0.131,-17.354 | |
| 1877 | +2024-06-11,60.166,13.123,3.319,20.916,-3.292,6.902,-9.466,-17.953,5.464,-0.933,-18.080 | |
| 1878 | +2024-06-12,60.232,12.958,3.315,22.341,-4.651,7.773,-9.586,-20.068,6.400,0.195,-18.676 | |
| 1879 | +2024-06-13,59.898,13.335,3.367,20.080,-3.621,5.646,-9.262,-18.289,5.963,0.385,-17.605 | |
| 1880 | +2024-06-14,59.342,14.046,3.634,15.629,-3.243,2.473,-9.213,-13.079,6.988,0.859,-18.093 | |
| 1881 | +2024-06-17,59.316,14.208,3.858,14.832,-4.387,2.869,-9.510,-11.289,7.082,0.476,-18.139 | |
| 1882 | +2024-06-18,59.588,14.205,4.164,13.944,-4.009,3.919,-10.444,-10.664,7.575,0.079,-18.770 | |
| 1883 | +2024-06-20,59.398,13.922,4.097,12.651,-4.067,3.682,-10.403,-10.082,8.056,0.276,-18.132 | |
| 1884 | +2024-06-21,59.412,13.846,4.384,12.353,-4.525,3.313,-10.211,-10.875,8.676,0.768,-17.729 | |
| 1885 | +2024-06-24,59.333,13.708,3.802,12.340,-3.598,4.704,-10.418,-11.276,8.534,0.062,-17.858 | |
| 1886 | +2024-06-25,59.530,13.471,3.099,11.959,-4.393,5.041,-10.693,-9.433,8.868,0.440,-18.358 | |
| 1887 | +2024-06-26,59.571,13.640,3.457,11.985,-4.226,3.390,-10.927,-8.732,9.179,1.094,-18.861 | |
| 1888 | +2024-06-27,59.578,13.897,3.360,10.024,-4.994,2.054,-10.573,-6.542,9.500,1.882,-18.608 | |
| 1889 | +2024-06-28,59.509,14.040,3.511,10.956,-4.352,3.161,-10.789,-8.704,9.233,1.188,-18.243 | |
| 1890 | +2024-07-01,59.444,13.827,2.941,10.869,-3.934,3.443,-10.006,-8.927,8.971,1.559,-18.741 | |
| 1891 | +2024-07-02,59.411,13.976,2.820,9.671,-3.921,2.239,-9.543,-7.251,9.266,1.696,-18.952 | |
| 1892 | +2024-07-03,59.260,13.947,3.032,9.451,-4.604,1.468,-8.692,-6.718,9.118,1.452,-18.453 | |
| 1893 | +2024-07-05,59.345,12.938,1.910,9.832,-4.565,0.812,-9.265,-6.198,9.784,2.983,-18.230 | |
| 1894 | +2024-07-08,59.471,15.110,4.477,10.482,-6.057,2.658,-11.107,-5.514,7.521,0.414,-17.985 | |
| 1895 | +2024-07-09,59.870,17.139,5.813,11.112,-6.555,4.093,-11.278,-4.280,4.933,-2.850,-18.126 | |
| 1896 | +2024-07-10,60.204,16.898,5.636,11.987,-5.990,4.867,-10.731,-2.436,3.802,-3.571,-20.464 | |
| 1897 | +2024-07-11,60.733,16.842,5.775,13.540,-6.640,6.815,-7.940,-4.325,2.264,-6.022,-20.308 | |
| 1898 | +2024-07-12,60.529,16.654,4.769,13.047,-5.962,6.226,-7.868,-4.298,2.672,-6.204,-19.037 | |
| 1899 | +2024-07-15,60.500,15.891,4.038,14.801,-6.985,7.028,-7.268,-3.553,2.623,-6.722,-19.853 | |
| 1900 | +2024-07-16,60.526,15.895,3.902,14.404,-6.861,6.632,-6.355,-3.096,2.247,-6.799,-19.970 | |
| 1901 | +2024-07-17,60.333,16.440,5.015,13.472,-8.494,5.819,-5.602,-2.878,2.312,-6.610,-19.472 | |
| 1902 | +2024-07-18,60.176,17.197,6.680,11.854,-9.391,4.313,-6.369,-1.754,2.306,-6.383,-18.452 | |
| 1903 | +2024-07-19,59.698,17.811,7.946,9.515,-9.263,1.886,-6.204,-3.028,2.730,-5.333,-16.062 | |
| 1904 | +2024-07-22,59.762,17.780,7.855,9.556,-9.566,2.088,-6.709,-3.404,2.870,-5.346,-15.125 | |
| 1905 | +2024-07-23,59.569,17.787,7.685,8.985,-9.515,1.996,-7.568,-3.324,3.001,-4.704,-14.343 | |
| 1906 | +2024-07-24,59.372,17.451,7.507,7.539,-7.942,1.172,-7.657,-1.285,3.023,-5.127,-14.681 | |
| 1907 | +2024-07-25,59.937,18.000,8.916,4.975,-7.752,-0.751,-8.869,0.644,0.979,-5.164,-10.978 | |
| 1908 | +2024-07-26,60.125,17.477,8.644,5.928,-9.157,0.278,-6.751,-0.153,1.279,-6.395,-11.149 | |
| 1909 | +2024-07-29,60.148,17.319,8.395,6.835,-8.347,0.435,-7.165,-0.841,1.832,-6.863,-11.599 | |
| 1910 | +2024-07-30,60.237,16.885,8.327,6.098,-9.565,0.256,-6.787,1.311,4.159,-10.291,-10.393 | |
| 1911 | +2024-07-31,60.689,17.857,10.098,4.062,-11.204,-1.097,-8.276,3.826,3.893,-11.089,-8.070 | |
| 1912 | +2024-08-01,60.921,17.953,10.178,3.664,-10.732,-1.481,-8.960,5.098,3.930,-11.202,-8.448 | |
| 1913 | +2024-08-02,62.081,18.783,12.477,3.150,-12.902,-1.960,-9.767,3.637,3.859,-10.611,-6.666 | |
| 1914 | +2024-08-05,66.654,20.388,18.988,-1.195,-13.873,-3.932,-11.809,-1.766,-1.384,-8.192,2.775 | |
| 1915 | +2024-08-06,66.568,21.382,19.778,-0.978,-15.444,-4.007,-11.891,-1.104,-1.497,-8.958,2.718 | |
| 1916 | +2024-08-07,66.353,21.237,18.915,1.978,-13.824,-1.403,-11.530,-2.104,-2.352,-10.733,-0.185 | |
| 1917 | +2024-08-08,66.439,21.439,18.232,3.478,-11.583,0.164,-10.521,-5.070,-2.584,-11.856,-1.700 | |
| 1918 | +2024-08-09,66.220,19.578,16.174,5.282,-12.066,0.675,-10.128,-5.060,0.563,-9.568,-5.450 | |
| 1919 | +2024-08-12,66.220,19.430,15.950,5.305,-10.762,0.807,-10.179,-5.802,0.469,-9.658,-5.560 | |
| 1920 | +2024-08-13,66.065,19.193,15.400,5.850,-10.282,1.378,-9.571,-5.617,-0.586,-10.049,-5.715 | |
| 1921 | +2024-08-14,65.922,18.653,14.684,5.768,-10.154,1.629,-9.701,-6.025,0.466,-9.823,-5.498 | |
| 1922 | +2024-08-15,65.861,19.313,15.135,4.811,-10.640,1.992,-10.081,-5.417,0.668,-9.626,-6.155 | |
| 1923 | +2024-08-16,65.865,19.164,15.389,3.935,-10.083,1.812,-10.296,-6.438,0.697,-9.356,-4.823 | |
| 1924 | +2024-08-19,65.701,19.340,16.195,2.362,-9.805,0.982,-10.271,-3.424,-0.874,-10.435,-4.069 | |
| 1925 | +2024-08-20,65.621,19.052,16.004,2.264,-9.875,0.941,-10.452,-3.007,-0.390,-10.404,-4.134 | |
| 1926 | +2024-08-21,65.740,19.084,15.947,1.909,-9.679,0.700,-10.476,-2.645,-0.513,-10.353,-3.975 | |
| 1927 | +2024-08-22,65.977,20.040,16.569,2.000,-9.600,1.514,-9.363,-4.362,-0.808,-9.651,-6.338 | |
| 1928 | +2024-08-23,65.969,20.954,17.454,2.253,-13.171,1.414,-9.926,-3.196,-0.129,-9.792,-5.863 | |
| 1929 | +2024-08-26,66.053,21.070,16.805,1.548,-13.419,0.477,-9.972,-1.275,-0.405,-8.651,-6.178 | |
| 1930 | +2024-08-27,65.570,19.337,16.192,1.198,-11.944,2.510,-9.791,1.796,-0.273,-10.571,-8.455 | |
| 1931 | +2024-08-28,66.125,19.845,17.724,1.366,-10.872,2.970,-9.700,-1.714,-0.975,-10.388,-8.256 | |
| 1932 | +2024-08-29,66.049,19.493,18.221,0.386,-11.586,2.188,-10.062,-0.823,-0.382,-9.505,-7.930 | |
| 1933 | +2024-08-30,65.962,19.984,17.731,0.706,-10.485,3.092,-9.482,-2.503,-0.553,-9.990,-8.500 | |
| 1934 | +2024-09-03,66.072,19.337,17.828,0.172,-11.065,2.062,-9.696,0.487,-1.204,-10.435,-7.486 | |
| 1935 | +2024-09-04,66.140,18.184,17.740,-1.722,-12.397,-1.614,-10.662,6.246,-2.616,-10.786,-2.373 | |
| 1936 | +2024-09-05,65.709,18.006,16.524,-0.826,-13.152,-0.394,-9.723,5.025,-1.549,-10.121,-3.789 | |
| 1937 | +2024-09-06,65.250,16.292,16.512,-0.571,-13.501,-0.528,-11.334,9.535,-2.289,-10.195,-3.922 | |
| 1938 | +2024-09-09,65.432,18.274,18.125,0.091,-12.766,0.596,-10.218,5.416,-2.610,-10.358,-6.549 | |
| 1939 | +2024-09-10,65.300,17.789,17.644,-0.968,-13.127,-0.443,-10.314,6.387,-2.364,-10.142,-4.462 | |
| 1940 | +2024-09-11,65.263,17.840,17.812,-1.474,-12.929,-1.085,-10.595,6.643,-2.447,-10.122,-3.644 | |
| 1941 | +2024-09-12,65.391,18.559,17.875,-0.797,-12.684,-1.518,-9.657,2.318,-3.398,-9.613,-1.086 | |
| 1942 | +2024-09-13,65.368,19.004,19.297,0.844,-14.130,-0.095,-8.846,4.495,-4.997,-12.830,-2.743 | |
| 1943 | +2024-09-16,65.567,19.195,19.082,0.395,-13.339,-0.430,-10.161,3.067,-4.185,-11.780,-1.843 | |
| 1944 | +2024-09-17,65.612,19.923,19.340,1.192,-13.526,0.901,-10.343,1.037,-4.327,-12.941,-1.256 | |
| 1945 | +2024-09-18,65.961,19.102,19.281,0.785,-12.379,-0.547,-9.107,1.459,-3.972,-13.005,-1.618 | |
| 1946 | +2024-09-19,66.047,19.875,20.128,0.045,-12.624,-2.479,-9.007,1.183,-3.703,-12.864,-0.552 | |
| 1947 | +2024-09-20,65.897,20.540,21.078,-0.789,-13.927,-3.488,-10.252,3.080,-3.417,-12.897,0.072 | |
| 1948 | +2024-09-23,66.176,21.031,21.037,-0.054,-13.437,-2.450,-10.481,0.943,-3.104,-14.916,1.431 | |
| 1949 | +2024-09-24,66.217,20.775,20.413,-0.486,-14.370,-2.409,-11.195,1.323,-1.565,-13.174,0.687 | |
| 1950 | +2024-09-25,66.395,20.794,20.302,-0.412,-14.385,-2.401,-10.957,1.008,-1.565,-13.634,1.250 | |
| 1951 | +2024-09-26,66.587,17.312,19.006,1.399,-12.550,-1.135,-9.432,2.150,-1.843,-14.157,-0.749 | |
| 1952 | +2024-09-27,66.297,18.675,20.305,-1.834,-15.043,-3.462,-11.401,5.634,-0.900,-14.085,2.111 | |
| 1953 | +2024-09-30,66.385,18.484,20.164,-1.926,-14.820,-3.710,-11.210,6.170,-0.998,-14.129,1.975 | |
| 1954 | +2024-10-01,66.960,15.076,17.953,-2.144,-13.195,-3.707,-8.204,9.619,-2.185,-13.894,0.681 | |
| 1955 | +2024-10-02,67.004,16.628,18.642,-1.599,-13.039,-3.762,-9.202,7.476,-3.094,-14.046,1.996 | |
| 1956 | +2024-10-03,67.050,16.078,18.542,-2.289,-13.717,-4.602,-8.525,8.701,-2.577,-13.841,2.228 | |
| 1957 | +2024-10-04,66.709,16.627,18.159,-3.608,-13.066,-4.817,-8.818,8.209,-1.579,-12.683,1.576 | |
| 1958 | +2024-10-07,66.888,16.797,19.413,-3.836,-14.143,-4.926,-8.442,8.230,-2.240,-13.179,2.326 | |
| 1959 | +2024-10-08,66.436,16.606,18.706,-4.215,-13.931,-4.820,-8.584,9.677,-1.981,-13.073,1.614 | |
| 1960 | +2024-10-09,66.877,18.199,19.027,-2.517,-12.321,-3.769,-10.610,3.323,-2.022,-11.692,2.383 | |
| 1961 | +2024-10-10,66.993,19.720,20.971,-1.942,-13.208,-3.773,-10.465,0.396,-1.948,-13.167,3.416 | |
| 1962 | +2024-10-11,67.332,21.855,24.579,-0.947,-15.203,-3.262,-9.536,-6.535,-2.721,-12.439,4.210 | |
| 1963 | +2024-10-14,66.945,22.650,25.765,-0.928,-16.561,-2.305,-9.876,-4.231,-4.616,-14.136,4.239 | |
| 1964 | +2024-10-15,66.713,21.408,24.723,-1.698,-16.647,-2.527,-9.805,-2.432,-2.914,-12.600,2.491 | |
| 1965 | +2024-10-16,66.882,22.940,25.139,-0.085,-15.684,-3.673,-9.121,-5.495,-4.759,-13.107,3.845 | |
| 1966 | +2024-10-17,66.883,22.918,25.427,-0.042,-15.721,-3.662,-9.162,-5.376,-4.833,-12.766,3.217 | |
| 1967 | +2024-10-18,66.903,23.286,25.630,-0.389,-16.473,-4.480,-8.974,-7.205,-5.051,-12.380,6.036 | |
| 1968 | +2024-10-21,66.851,22.876,25.282,-0.607,-16.384,-4.652,-9.026,-5.694,-4.982,-11.982,5.169 | |
| 1969 | +2024-10-22,66.670,22.866,26.272,-1.048,-17.093,-3.954,-7.681,-6.216,-5.836,-12.878,5.568 | |
| 1970 | +2024-10-23,66.605,22.947,26.488,-0.850,-16.977,-3.610,-7.349,-6.002,-7.039,-13.506,5.899 | |
| 1971 | +2024-10-24,66.445,22.833,27.159,-2.292,-18.381,-3.652,-7.235,-5.584,-5.320,-13.105,5.577 | |
| 1972 | +2024-10-25,66.431,22.983,27.162,-1.834,-18.076,-3.634,-6.822,-5.975,-5.887,-13.268,5.352 | |
| 1973 | +2024-10-28,66.458,23.431,27.721,-1.867,-18.249,-3.600,-7.077,-6.237,-6.137,-14.138,6.153 | |
| 1974 | +2024-10-29,66.417,23.536,27.946,-2.119,-18.310,-3.842,-7.244,-6.348,-6.069,-14.066,6.517 | |
| 1975 | +2024-10-30,66.417,23.880,28.179,-2.297,-17.929,-4.024,-6.287,-6.371,-6.445,-14.107,5.399 | |
| 1976 | +2024-10-31,66.516,23.549,27.904,-2.343,-17.707,-3.579,-7.568,-6.594,-6.089,-13.929,6.357 | |
| 1977 | +2024-11-01,66.570,23.811,27.817,-2.750,-18.227,-3.801,-7.244,-5.727,-7.104,-13.821,7.045 | |
| 1978 | +2024-11-04,66.515,24.085,28.079,-1.861,-17.594,-3.753,-7.589,-5.484,-7.312,-14.297,5.727 | |
| 1979 | +2024-11-05,66.224,23.920,28.120,-2.994,-17.461,-3.524,-8.134,-5.497,-6.147,-13.157,4.875 | |
| 1980 | +2024-11-06,67.289,25.926,29.648,0.252,-17.285,-1.360,-6.035,-10.954,-7.578,-14.444,1.830 | |
| 1981 | +2024-11-07,66.987,25.628,29.889,-0.194,-17.506,-1.544,-6.517,-10.949,-7.323,-14.406,2.921 | |
| 1982 | +2024-11-08,66.240,25.818,30.487,-3.513,-20.406,-3.066,-7.551,-9.124,-5.767,-14.487,7.610 | |
| 1983 | +2024-11-11,66.298,25.984,30.758,-3.656,-19.908,-2.716,-6.786,-9.248,-7.661,-14.096,7.328 | |
| 1984 | +2024-11-12,66.659,25.402,29.688,-0.911,-18.274,-1.408,-4.455,-11.166,-9.030,-14.744,4.897 | |
| 1985 | +2024-11-13,67.067,24.730,28.253,1.748,-17.263,-0.150,-2.215,-12.419,-9.090,-15.276,1.683 | |
| 1986 | +2024-11-14,66.991,24.716,28.436,1.658,-17.722,-0.503,-2.596,-10.869,-9.294,-15.723,1.898 | |
| 1987 | +2024-11-15,66.978,24.811,28.631,3.397,-16.915,-0.188,-3.246,-11.229,-10.075,-16.312,1.126 | |
| 1988 | +2024-11-18,66.923,25.007,29.041,4.090,-15.716,-0.357,-3.885,-12.533,-10.525,-16.523,1.401 | |
| 1989 | +2024-11-19,66.816,25.034,28.593,4.876,-13.749,-0.967,-4.862,-14.372,-10.582,-16.752,2.780 | |
| 1990 | +2024-11-20,66.253,23.583,27.044,3.318,-13.677,-1.170,-4.399,-10.855,-8.551,-15.353,0.060 | |
| 1991 | +2024-11-21,66.022,22.571,27.953,3.797,-11.264,-3.146,-1.437,-12.023,-11.127,-16.286,0.962 | |
| 1992 | +2024-11-22,66.199,23.452,28.719,3.754,-11.389,-2.999,-2.347,-15.121,-10.863,-16.616,3.409 | |
| 1993 | +2024-11-25,66.384,23.662,29.034,6.128,-10.797,-2.012,-3.673,-17.516,-11.918,-17.327,4.420 | |
| 1994 | +2024-11-26,66.462,24.090,29.267,5.224,-10.736,-2.516,-4.045,-17.205,-11.737,-17.211,4.868 | |
| 1995 | +2024-11-27,66.481,22.385,27.195,4.319,-11.079,-3.328,-2.241,-16.403,-9.616,-15.666,4.436 | |
| 1996 | +2024-11-29,66.565,25.657,29.278,-0.018,-15.039,-3.930,-6.696,-12.947,-8.785,-14.609,7.090 | |
| 1997 | +2024-12-02,66.504,24.417,29.071,1.023,-14.442,-3.601,-6.920,-13.419,-8.632,-14.513,7.016 | |
| 1998 | +2024-12-03,66.187,25.975,30.408,0.071,-17.569,-3.992,-9.479,-10.721,-9.139,-13.848,8.294 | |
| 1999 | +2024-12-04,65.981,26.906,31.139,0.546,-19.460,-3.290,-11.214,-11.218,-8.716,-14.181,9.488 | |
| 2000 | +2024-12-05,65.972,26.089,31.023,1.260,-20.224,-1.812,-11.650,-11.543,-8.946,-13.646,9.449 | |
| 2001 | +2024-12-06,66.133,26.712,31.399,1.633,-19.739,-1.208,-10.473,-11.905,-11.852,-13.998,9.431 | |
| 2002 | +2024-12-09,66.139,26.730,31.638,1.327,-19.429,-1.813,-7.788,-12.500,-13.257,-16.106,11.197 | |
| 2003 | +2024-12-10,66.096,26.857,31.264,0.862,-19.639,-1.937,-7.734,-13.145,-12.771,-15.185,11.428 | |
| 2004 | +2024-12-11,65.850,26.715,31.551,0.994,-19.938,-1.502,-8.158,-13.010,-12.556,-15.570,11.473 | |
| 2005 | +2024-12-12,65.522,25.596,32.547,3.119,-18.232,-0.643,-7.396,-14.135,-15.331,-16.734,11.210 | |
| 2006 | +2024-12-13,65.427,26.215,32.539,3.019,-18.071,-1.037,-7.481,-13.744,-15.729,-16.432,10.721 | |
| 2007 | +2024-12-16,65.639,26.519,31.064,2.587,-17.909,-0.872,-7.849,-13.500,-14.237,-15.993,10.189 | |
| 2008 | +2024-12-17,65.485,27.393,31.358,2.098,-18.250,-0.504,-7.889,-15.128,-13.832,-15.929,10.683 | |
| 2009 | +2024-12-18,66.037,28.870,34.601,2.881,-20.332,1.143,-6.656,-19.327,-15.421,-17.653,11.895 | |
| 2010 | +2024-12-19,65.983,29.075,34.689,3.790,-20.689,2.652,-6.076,-17.463,-18.560,-19.427,12.008 | |
| 2011 | +2024-12-20,65.645,30.875,35.282,3.858,-21.423,3.604,-6.626,-16.243,-20.018,-19.985,10.675 | |
| 2012 | +2024-12-23,65.571,27.805,32.006,2.298,-19.729,1.255,-2.563,-15.278,-17.373,-18.803,10.383 | |
| 2013 | +2024-12-24,65.977,26.056,28.459,2.941,-17.003,1.894,1.854,-12.659,-16.001,-17.370,1.829 | |
| 2014 | +2024-12-26,65.555,25.539,28.386,2.055,-16.867,1.382,1.894,-12.725,-15.549,-16.722,2.606 | |
| 2015 | +2024-12-27,65.224,25.370,27.893,1.719,-16.874,1.296,0.834,-10.756,-16.197,-16.993,3.707 | |
| 2016 | +2024-12-30,65.059,26.844,29.515,2.114,-18.300,2.197,1.445,-12.768,-19.130,-20.584,8.667 | |
| 2017 | +2024-12-31,64.851,25.915,27.968,2.767,-17.288,2.807,1.979,-10.069,-19.661,-20.113,5.695 | |
| 2018 | +2025-01-02,65.042,27.284,29.537,3.131,-18.176,3.819,0.682,-11.779,-20.357,-20.384,6.242 | |
| 2019 | +2025-01-03,65.119,25.389,26.641,2.361,-17.462,2.982,2.528,-10.642,-18.148,-18.594,4.945 | |
| 2020 | +2025-01-06,65.255,25.590,26.676,3.280,-17.369,3.988,1.799,-11.838,-18.691,-18.622,5.186 | |
| 2021 | +2025-01-07,65.182,26.040,26.717,4.343,-17.329,5.557,1.645,-11.188,-20.065,-19.605,3.886 | |
| 2022 | +2025-01-08,64.785,25.999,25.400,4.601,-17.115,5.420,2.928,-10.596,-19.433,-18.814,1.611 | |
| 2023 | +2025-01-09,64.712,25.167,24.075,4.814,-13.978,1.350,2.027,-9.308,-19.837,-18.590,4.280 | |
| 2024 | +2025-01-10,65.496,28.018,26.867,2.255,-14.030,3.020,1.386,-12.801,-20.493,-20.229,6.007 | |
| 2025 | +2025-01-13,65.520,28.005,27.101,2.633,-14.904,2.762,1.868,-13.230,-20.318,-20.255,6.338 | |
| 2026 | +2025-01-14,65.458,27.940,27.570,2.502,-14.426,3.384,0.553,-13.331,-20.133,-20.217,6.158 | |
| 2027 | +2025-01-15,65.816,28.718,28.738,2.251,-14.398,5.990,-1.240,-13.743,-21.304,-20.945,5.933 | |
| 2028 | +2025-01-16,65.977,27.608,27.208,1.951,-14.653,5.040,-0.136,-13.271,-20.051,-20.303,6.606 | |
| 2029 | +2025-01-17,66.153,27.760,27.402,1.878,-15.182,4.643,0.211,-12.969,-19.927,-20.314,6.499 | |
| 2030 | +2025-01-21,65.289,25.072,26.236,5.621,-9.967,5.623,-5.056,-12.142,-19.674,-20.057,4.344 | |
| 2031 | +2025-01-22,65.799,24.101,23.949,5.639,-10.436,4.384,-3.603,-11.109,-20.159,-19.781,7.015 | |
| 2032 | +2025-01-23,65.955,24.147,24.531,5.256,-10.531,4.120,-4.149,-11.677,-19.407,-19.396,7.105 | |
| 2033 | +2025-01-24,65.814,24.711,25.363,4.684,-8.706,3.682,-5.874,-11.680,-19.819,-18.793,6.431 | |
| 2034 | +2025-01-27,66.122,24.576,25.321,5.838,-7.782,4.901,-7.301,-13.204,-19.177,-17.279,4.105 | |
| 2035 | +2025-01-28,65.961,23.909,24.911,5.754,-7.433,4.781,-7.538,-12.496,-18.609,-16.937,3.657 | |
| 2036 | +2025-01-29,65.412,22.551,23.964,5.449,-6.246,5.095,-7.751,-11.730,-17.846,-15.882,2.397 | |
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added
results/rev_rolling_w250.csv
+2266 −0
@@ -0,0 +1,2266 @@ | ||
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| 1745 | +2024-02-13,64.793,29.059,14.156,4.788,-10.377,0.010,5.632,-18.688,-3.745,-1.756,-19.080 | |
| 1746 | +2024-02-14,64.752,29.197,14.706,4.168,-11.097,-0.017,5.141,-19.338,-2.654,-0.663,-19.443 | |
| 1747 | +2024-02-15,64.762,29.027,14.933,5.058,-10.699,0.093,5.102,-19.880,-2.835,-0.601,-20.198 | |
| 1748 | +2024-02-16,64.763,28.925,14.449,5.578,-10.618,0.022,5.195,-19.381,-3.343,-1.268,-19.558 | |
| 1749 | +2024-02-20,64.631,29.084,14.509,5.423,-10.169,0.442,4.619,-18.909,-3.690,-1.873,-19.436 | |
| 1750 | +2024-02-21,64.599,29.097,14.253,5.582,-9.842,1.043,4.696,-18.976,-3.796,-2.165,-19.894 | |
| 1751 | +2024-02-22,64.518,28.459,13.388,5.754,-9.663,0.428,5.114,-18.682,-3.666,-2.304,-18.828 | |
| 1752 | +2024-02-23,64.979,29.003,13.691,7.437,-8.197,3.750,5.902,-21.449,-4.953,-3.814,-21.369 | |
| 1753 | +2024-02-26,65.266,28.777,13.285,9.199,-7.746,4.865,5.981,-21.372,-5.218,-4.393,-23.378 | |
| 1754 | +2024-02-27,65.380,29.046,13.324,10.601,-6.345,8.041,4.661,-24.257,-5.921,-3.964,-25.186 | |
| 1755 | +2024-02-28,64.830,26.625,11.131,8.523,-8.157,4.086,3.001,-22.224,-1.013,0.867,-22.839 | |
| 1756 | +2024-02-29,64.587,26.353,11.021,5.989,-8.697,1.056,1.445,-22.473,3.057,4.128,-21.879 | |
| 1757 | +2024-03-01,64.468,24.921,9.537,8.155,-9.716,0.968,1.863,-20.901,1.965,3.594,-20.386 | |
| 1758 | +2024-03-04,63.607,22.826,7.512,9.296,-11.517,-0.044,1.087,-20.261,3.185,4.323,-16.407 | |
| 1759 | +2024-03-05,60.985,16.622,3.686,7.393,-12.822,-2.008,2.734,-13.654,6.158,4.373,-12.481 | |
| 1760 | +2024-03-06,60.943,16.183,4.352,9.966,-10.967,1.375,1.630,-13.278,1.664,0.851,-11.776 | |
| 1761 | +2024-03-07,59.448,15.019,3.502,10.662,-11.027,1.449,2.115,-9.509,-0.452,0.930,-12.688 | |
| 1762 | +2024-03-08,58.777,14.828,4.733,9.010,-10.074,2.321,1.156,-6.917,-2.726,-1.418,-10.912 | |
| 1763 | +2024-03-11,58.697,14.781,5.248,10.780,-7.895,3.765,0.589,-5.952,-7.045,-4.275,-9.995 | |
| 1764 | +2024-03-12,58.494,13.919,4.732,12.244,-6.325,6.578,0.177,-6.900,-9.001,-4.449,-10.976 | |
| 1765 | +2024-03-13,58.840,14.343,5.013,14.293,-7.660,6.254,0.949,-6.615,-9.679,-5.442,-11.456 | |
| 1766 | +2024-03-14,58.409,13.214,4.433,14.893,-5.275,7.036,-1.309,-7.448,-9.675,-3.996,-11.874 | |
| 1767 | +2024-03-15,58.774,11.404,2.594,18.149,-3.580,9.407,-1.571,-7.912,-10.858,-5.358,-12.274 | |
| 1768 | +2024-03-18,58.481,9.819,2.832,16.492,-2.829,8.922,-3.233,-4.867,-10.196,-3.408,-13.532 | |
| 1769 | +2024-03-19,59.055,9.191,1.956,21.572,-3.188,12.649,-3.304,-6.897,-12.473,-5.016,-14.491 | |
| 1770 | +2024-03-20,59.270,10.777,3.010,21.987,-2.528,13.942,-2.154,-8.380,-14.179,-8.131,-14.345 | |
| 1771 | +2024-03-21,59.148,10.978,3.258,21.647,-3.438,12.991,-2.173,-9.261,-13.170,-7.116,-13.715 | |
| 1772 | +2024-03-22,59.458,11.073,3.795,22.770,-3.323,13.074,-2.932,-9.550,-13.838,-7.303,-13.766 | |
| 1773 | +2024-03-25,59.331,10.545,3.254,22.194,-3.570,12.436,-2.725,-9.118,-12.442,-6.383,-14.190 | |
| 1774 | +2024-03-26,59.434,10.738,3.738,22.436,-2.960,13.077,-4.994,-7.610,-13.345,-6.769,-14.312 | |
| 1775 | +2024-03-27,59.510,10.796,3.891,23.894,-3.162,13.620,-5.744,-7.690,-13.752,-7.536,-14.315 | |
| 1776 | +2024-03-28,59.662,10.459,3.677,25.513,-1.945,14.388,-6.686,-8.439,-13.659,-7.810,-15.499 | |
| 1777 | +2024-04-01,59.419,8.819,2.701,23.853,-1.825,13.258,-5.615,-9.776,-10.770,-4.010,-16.634 | |
| 1778 | +2024-04-02,59.655,9.008,3.381,24.728,0.990,14.373,-6.438,-8.735,-13.822,-7.022,-16.463 | |
| 1779 | +2024-04-03,59.433,8.311,2.382,24.579,1.266,13.858,-7.042,-8.718,-11.980,-5.524,-17.132 | |
| 1780 | +2024-04-04,58.926,7.520,2.090,23.927,2.680,14.162,-7.981,-7.635,-12.757,-5.366,-16.640 | |
| 1781 | +2024-04-05,59.001,7.212,1.595,24.385,2.026,13.718,-7.413,-9.017,-11.140,-4.310,-17.057 | |
| 1782 | +2024-04-08,59.081,8.102,3.023,26.247,2.776,14.887,-8.849,-7.821,-13.094,-7.930,-17.341 | |
| 1783 | +2024-04-09,58.953,7.512,2.693,25.875,4.414,14.540,-10.518,-7.950,-12.864,-6.647,-17.055 | |
| 1784 | +2024-04-10,59.667,10.023,5.279,21.993,3.196,13.888,-9.543,-8.719,-12.828,-6.195,-17.094 | |
| 1785 | +2024-04-11,59.700,10.511,5.364,21.822,2.544,14.424,-9.159,-7.938,-12.543,-6.428,-18.598 | |
| 1786 | +2024-04-12,59.589,9.894,3.868,21.691,2.842,14.798,-8.376,-8.393,-12.027,-5.468,-18.831 | |
| 1787 | +2024-04-15,60.008,9.729,2.871,22.249,3.253,15.154,-6.070,-9.684,-12.409,-6.120,-18.972 | |
| 1788 | +2024-04-16,59.589,9.588,2.492,20.714,2.325,13.341,-5.882,-7.691,-11.474,-4.925,-18.488 | |
| 1789 | +2024-04-17,59.485,10.199,2.298,20.549,2.497,13.201,-6.524,-8.096,-11.219,-4.065,-18.838 | |
| 1790 | +2024-04-18,59.611,10.342,2.460,21.176,3.210,12.607,-5.271,-8.764,-12.205,-5.286,-18.269 | |
| 1791 | +2024-04-19,59.518,11.034,2.214,21.460,3.903,13.432,-6.337,-9.643,-12.836,-5.847,-17.378 | |
| 1792 | +2024-04-22,59.284,11.136,2.975,19.074,4.032,12.575,-7.466,-8.920,-11.394,-4.440,-17.573 | |
| 1793 | +2024-04-23,59.324,10.668,2.380,21.590,2.791,13.464,-6.955,-8.537,-12.926,-5.087,-17.388 | |
| 1794 | +2024-04-24,59.174,10.207,3.474,18.279,3.696,12.333,-8.967,-7.630,-10.110,-2.585,-18.698 | |
| 1795 | +2024-04-25,58.952,10.562,4.372,18.053,5.240,13.512,-11.336,-5.758,-11.555,-3.583,-19.508 | |
| 1796 | +2024-04-26,58.252,10.845,5.210,16.707,3.491,14.679,-12.601,-4.970,-10.923,-4.887,-17.551 | |
| 1797 | +2024-04-29,57.930,9.187,2.963,17.814,5.890,13.326,-12.277,-4.992,-11.251,-4.520,-16.139 | |
| 1798 | +2024-04-30,57.586,8.751,1.844,20.587,1.526,13.207,-10.962,-6.100,-10.561,-3.581,-14.711 | |
| 1799 | +2024-05-01,57.997,9.938,3.239,21.284,3.136,14.511,-10.582,-8.495,-12.913,-4.935,-15.183 | |
| 1800 | +2024-05-02,57.635,9.320,2.137,21.145,0.855,13.815,-9.495,-8.662,-10.217,-1.972,-16.927 | |
| 1801 | +2024-05-03,57.526,10.593,2.792,21.434,-1.905,14.098,-7.989,-7.776,-11.583,-3.660,-16.004 | |
| 1802 | +2024-05-06,57.543,9.686,2.125,20.740,-0.932,14.235,-8.033,-7.766,-10.944,-2.725,-16.385 | |
| 1803 | +2024-05-07,57.638,9.498,2.585,20.271,-0.958,14.869,-9.515,-7.201,-10.736,-2.202,-16.611 | |
| 1804 | +2024-05-08,58.355,10.482,4.591,21.894,-1.718,16.867,-9.992,-7.301,-12.408,-5.198,-17.216 | |
| 1805 | +2024-05-09,58.331,10.133,3.432,22.010,-1.362,15.096,-9.699,-8.366,-10.090,-3.343,-17.810 | |
| 1806 | +2024-05-10,58.613,9.654,2.687,23.264,-0.837,15.292,-9.746,-8.719,-10.085,-2.947,-18.563 | |
| 1807 | +2024-05-13,58.739,9.229,2.409,23.536,-0.687,14.904,-10.038,-8.366,-9.765,-2.657,-18.565 | |
| 1808 | +2024-05-14,58.494,9.220,2.705,23.016,-1.126,14.626,-9.583,-8.197,-9.420,-2.749,-18.492 | |
| 1809 | +2024-05-15,58.720,9.607,3.021,22.784,-0.947,15.273,-9.241,-9.729,-9.487,-3.055,-18.225 | |
| 1810 | +2024-05-16,58.769,9.811,4.662,23.992,-2.627,15.236,-8.962,-9.523,-10.194,-5.578,-16.816 | |
| 1811 | +2024-05-17,59.141,10.817,5.918,25.025,-4.458,15.919,-10.226,-9.534,-10.500,-6.138,-16.823 | |
| 1812 | +2024-05-20,59.238,11.140,6.529,27.375,-4.987,17.947,-11.167,-9.563,-12.890,-7.973,-16.411 | |
| 1813 | +2024-05-21,58.609,11.285,6.127,26.630,-6.186,15.964,-11.827,-7.603,-10.898,-7.302,-16.189 | |
| 1814 | +2024-05-22,58.247,10.166,4.533,24.914,-6.420,14.083,-11.722,-6.731,-7.665,-4.632,-16.525 | |
| 1815 | +2024-05-23,58.360,9.932,4.729,24.611,-6.031,13.868,-11.883,-5.530,-8.369,-4.990,-16.337 | |
| 1816 | +2024-05-24,58.436,9.610,4.044,24.836,-6.224,13.464,-10.878,-6.397,-6.773,-4.404,-17.279 | |
| 1817 | +2024-05-28,58.453,9.693,3.804,25.011,-5.891,13.260,-10.613,-7.512,-6.096,-4.013,-17.644 | |
| 1818 | +2024-05-29,58.312,9.076,3.044,23.444,-5.658,12.054,-10.304,-8.934,-3.368,-2.099,-17.255 | |
| 1819 | +2024-05-30,57.908,8.803,3.162,22.614,-4.742,10.779,-10.682,-6.929,-3.310,-2.467,-17.229 | |
| 1820 | +2024-05-31,58.164,8.289,3.091,23.093,-4.445,10.690,-11.424,-7.680,-3.035,-2.051,-16.528 | |
| 1821 | +2024-06-03,57.719,8.358,3.236,20.720,-4.334,8.650,-11.706,-3.708,-2.635,-2.054,-16.527 | |
| 1822 | +2024-06-04,57.804,9.352,4.418,21.880,-3.260,9.793,-10.850,-7.005,-3.349,-3.644,-17.335 | |
| 1823 | +2024-06-05,57.812,10.200,5.199,22.874,-3.561,10.415,-10.152,-8.591,-3.579,-3.895,-18.910 | |
| 1824 | +2024-06-06,57.728,10.139,5.000,22.623,-3.173,9.641,-10.066,-9.883,-2.527,-2.482,-19.272 | |
| 1825 | +2024-06-07,57.903,10.598,5.057,22.418,-3.282,10.072,-9.429,-10.904,-2.655,-2.484,-19.391 | |
| 1826 | +2024-06-10,58.040,10.521,4.894,23.259,-3.811,9.722,-9.111,-11.524,-1.687,-1.838,-20.424 | |
| 1827 | +2024-06-11,58.121,10.473,4.756,22.916,-3.595,9.945,-9.316,-10.850,-1.749,-2.555,-20.023 | |
| 1828 | +2024-06-12,58.356,10.169,4.822,23.788,-4.502,10.805,-9.395,-11.560,-1.787,-2.331,-20.008 | |
| 1829 | +2024-06-13,58.067,10.014,4.618,23.152,-3.986,9.428,-9.173,-11.118,-1.822,-1.660,-19.455 | |
| 1830 | +2024-06-14,57.887,10.918,4.877,23.033,-3.945,8.377,-9.562,-10.997,-1.152,-1.377,-20.171 | |
| 1831 | +2024-06-17,57.803,11.168,4.958,22.105,-4.780,7.748,-10.058,-8.995,-0.364,-1.352,-20.431 | |
| 1832 | +2024-06-18,58.059,11.409,5.879,20.785,-4.028,7.691,-10.712,-7.745,-1.311,-1.860,-20.108 | |
| 1833 | +2024-06-20,58.099,11.593,5.236,20.951,-3.679,7.915,-10.648,-8.920,-0.870,-1.732,-19.847 | |
| 1834 | +2024-06-21,58.054,11.283,5.182,20.836,-3.290,7.571,-10.002,-8.406,-1.279,-1.927,-19.969 | |
| 1835 | +2024-06-24,57.844,11.369,4.455,19.951,-3.084,7.401,-9.813,-6.545,-1.189,-2.086,-20.458 | |
| 1836 | +2024-06-25,58.249,11.585,4.170,19.983,-3.368,8.991,-10.276,-6.202,-1.182,-1.988,-21.713 | |
| 1837 | +2024-06-26,58.143,12.003,4.878,19.641,-4.314,7.508,-10.438,-4.209,-1.229,-1.760,-22.079 | |
| 1838 | +2024-06-27,58.208,13.316,5.302,19.165,-4.537,7.752,-10.292,-5.755,-0.946,-1.698,-22.307 | |
| 1839 | +2024-06-28,58.398,13.575,5.412,19.260,-4.440,8.040,-10.234,-7.098,-0.520,-1.589,-22.409 | |
| 1840 | +2024-07-01,58.430,13.118,4.824,19.350,-4.197,7.900,-9.756,-7.848,-0.261,-0.984,-22.146 | |
| 1841 | +2024-07-02,58.330,11.764,3.929,18.486,-4.215,7.861,-9.762,-6.690,0.272,-0.270,-21.375 | |
| 1842 | +2024-07-03,58.241,11.741,4.274,18.982,-5.165,8.171,-9.939,-6.324,0.293,-1.002,-21.030 | |
| 1843 | +2024-07-05,58.479,12.659,5.281,19.339,-6.875,9.517,-10.277,-6.188,-0.581,-1.904,-20.972 | |
| 1844 | +2024-07-08,58.945,14.557,8.666,19.839,-8.432,11.739,-11.551,-5.602,-2.726,-4.312,-22.179 | |
| 1845 | +2024-07-09,59.034,15.820,9.297,18.781,-9.274,10.785,-11.732,-4.977,-2.332,-4.179,-22.188 | |
| 1846 | +2024-07-10,59.504,16.151,9.762,19.455,-9.537,11.009,-11.864,-4.410,-2.750,-4.763,-23.053 | |
| 1847 | +2024-07-11,59.958,16.717,9.784,19.413,-9.784,12.400,-10.504,-6.082,-4.268,-6.440,-21.236 | |
| 1848 | +2024-07-12,59.829,16.173,9.203,19.348,-9.999,12.237,-10.330,-6.028,-3.563,-6.441,-20.602 | |
| 1849 | +2024-07-15,59.963,15.695,9.141,20.444,-10.843,12.709,-9.908,-6.494,-3.383,-6.153,-21.210 | |
| 1850 | +2024-07-16,59.809,16.329,8.829,19.628,-10.583,11.927,-9.985,-6.721,-3.305,-6.283,-19.836 | |
| 1851 | +2024-07-17,59.804,16.427,9.849,19.675,-11.472,11.805,-9.314,-7.209,-3.078,-6.339,-20.343 | |
| 1852 | +2024-07-18,59.691,17.404,10.561,18.457,-11.843,10.828,-9.637,-7.402,-3.442,-6.687,-18.240 | |
| 1853 | +2024-07-19,59.299,18.784,11.846,14.507,-12.388,8.359,-10.267,-6.252,-2.760,-6.324,-15.505 | |
| 1854 | +2024-07-22,59.271,18.846,11.596,13.640,-12.766,7.997,-9.485,-6.344,-2.355,-5.884,-15.244 | |
| 1855 | +2024-07-23,58.985,18.598,11.118,13.721,-11.847,7.829,-9.613,-6.189,-2.129,-5.587,-15.901 | |
| 1856 | +2024-07-24,58.839,18.258,10.976,12.963,-10.602,7.395,-10.136,-4.562,-2.394,-5.913,-15.986 | |
| 1857 | +2024-07-25,58.944,17.876,10.906,10.272,-8.990,5.790,-11.142,-2.370,-2.777,-5.995,-13.569 | |
| 1858 | +2024-07-26,58.625,17.824,10.835,9.458,-8.483,5.396,-10.210,-2.151,-2.502,-6.326,-13.842 | |
| 1859 | +2024-07-29,58.794,18.103,10.606,10.342,-8.119,5.564,-9.695,-4.851,-2.318,-5.968,-13.665 | |
| 1860 | +2024-07-30,58.750,18.332,11.403,9.435,-9.018,5.038,-10.072,-4.555,-2.280,-6.114,-12.167 | |
| 1861 | +2024-07-31,58.841,19.124,12.779,7.379,-9.139,3.468,-11.517,-1.268,-2.786,-6.708,-11.333 | |
| 1862 | +2024-08-01,58.947,19.252,13.342,6.733,-9.396,2.832,-12.100,0.349,-2.740,-6.663,-11.608 | |
| 1863 | +2024-08-02,59.493,20.790,15.351,6.045,-10.569,2.347,-12.151,-0.623,-2.910,-7.296,-10.985 | |
| 1864 | +2024-08-05,62.412,22.779,19.379,1.868,-15.597,-1.376,-12.327,-3.100,-1.913,-5.353,-4.360 | |
| 1865 | +2024-08-06,62.473,23.366,19.671,1.660,-16.647,-1.550,-12.390,-3.402,-1.477,-4.971,-4.260 | |
| 1866 | +2024-08-07,62.239,23.015,19.214,2.708,-16.032,-0.337,-12.062,-3.636,-1.749,-5.757,-5.366 | |
| 1867 | +2024-08-08,62.148,23.105,18.901,2.875,-15.405,-0.125,-11.766,-3.813,-2.214,-6.086,-5.474 | |
| 1868 | +2024-08-09,62.037,21.464,16.865,4.129,-13.317,0.969,-11.163,-3.911,-0.475,-6.134,-8.427 | |
| 1869 | +2024-08-12,62.021,21.523,16.769,4.169,-13.303,0.869,-11.424,-3.909,-0.442,-6.030,-8.223 | |
| 1870 | +2024-08-13,61.815,21.216,16.160,3.784,-13.126,1.087,-11.547,-3.642,-0.139,-5.598,-8.196 | |
| 1871 | +2024-08-14,61.815,21.165,16.115,3.740,-13.219,1.230,-11.727,-3.496,-0.245,-5.504,-8.058 | |
| 1872 | +2024-08-15,61.657,20.595,15.133,2.330,-13.497,0.053,-11.434,-3.192,1.318,-3.366,-7.940 | |
| 1873 | +2024-08-16,61.596,20.900,15.465,1.835,-13.323,-0.257,-11.659,-3.624,1.443,-2.914,-7.867 | |
| 1874 | +2024-08-19,61.442,19.982,14.734,0.819,-12.536,-1.065,-10.924,-2.043,0.976,-3.233,-6.712 | |
| 1875 | +2024-08-20,61.347,20.129,15.321,0.767,-12.581,-0.977,-11.244,-1.958,0.972,-3.280,-7.148 | |
| 1876 | +2024-08-21,61.346,19.661,14.901,0.504,-12.823,-1.224,-11.851,-1.413,2.130,-3.327,-6.557 | |
| 1877 | +2024-08-22,61.405,20.301,15.465,0.597,-12.809,-0.941,-11.577,-2.759,2.656,-2.692,-8.241 | |
| 1878 | +2024-08-23,61.398,20.431,16.136,1.087,-12.314,-0.410,-11.687,-3.736,2.856,-2.987,-9.376 | |
| 1879 | +2024-08-26,61.447,20.593,15.644,0.312,-12.365,-1.268,-11.427,-1.385,2.343,-3.173,-9.274 | |
| 1880 | +2024-08-27,61.297,20.115,14.486,-1.923,-11.887,-3.171,-10.758,2.700,2.344,-3.899,-8.007 | |
| 1881 | +2024-08-28,61.649,19.938,15.190,-1.593,-11.727,-2.877,-10.210,0.785,2.029,-3.827,-7.706 | |
| 1882 | +2024-08-29,61.857,19.632,15.799,-1.309,-12.023,-2.789,-10.653,0.027,2.504,-3.435,-7.753 | |
| 1883 | +2024-08-30,61.651,20.188,16.382,-1.393,-11.866,-2.462,-10.235,-1.553,2.205,-4.035,-7.231 | |
| 1884 | +2024-09-03,61.784,19.443,16.871,-2.399,-12.765,-3.603,-10.230,0.516,2.045,-4.218,-5.660 | |
| 1885 | +2024-09-04,61.851,17.961,16.432,-3.412,-13.492,-5.780,-10.568,4.067,1.461,-4.902,-1.767 | |
| 1886 | +2024-09-05,61.761,18.257,16.523,-2.260,-12.854,-4.168,-10.428,1.813,1.742,-4.961,-3.663 | |
| 1887 | +2024-09-06,62.057,17.895,16.550,-1.528,-12.836,-4.172,-10.934,0.942,1.533,-4.939,-2.512 | |
| 1888 | +2024-09-09,62.078,19.123,17.228,-1.294,-12.211,-3.400,-10.061,0.614,0.999,-5.244,-5.754 | |
| 1889 | +2024-09-10,62.000,18.956,17.136,-1.773,-12.490,-3.850,-10.316,0.325,1.030,-5.229,-3.788 | |
| 1890 | +2024-09-11,61.889,18.993,17.144,-1.942,-12.263,-4.014,-10.552,0.575,0.709,-5.608,-3.041 | |
| 1891 | +2024-09-12,61.849,19.154,17.163,-2.190,-11.856,-4.391,-10.085,1.283,0.061,-5.538,-3.602 | |
| 1892 | +2024-09-13,61.993,19.997,18.070,-0.857,-12.360,-3.558,-9.442,-0.807,-0.025,-6.243,-4.776 | |
| 1893 | +2024-09-16,62.115,19.838,17.869,0.173,-12.155,-3.309,-10.810,-0.908,-1.021,-5.688,-3.990 | |
| 1894 | +2024-09-17,62.231,20.237,18.292,0.522,-12.623,-2.669,-10.938,-2.093,-0.597,-6.017,-4.113 | |
| 1895 | +2024-09-18,62.668,20.455,18.276,0.860,-12.954,-2.405,-10.746,-2.530,-1.530,-7.133,-2.294 | |
| 1896 | +2024-09-19,62.545,19.853,17.774,1.236,-12.698,-2.637,-10.222,-0.386,-1.625,-7.094,-4.202 | |
| 1897 | +2024-09-20,62.419,20.002,18.205,0.529,-13.289,-3.848,-10.390,1.305,-1.107,-6.926,-4.482 | |
| 1898 | +2024-09-23,62.434,20.061,18.176,0.791,-13.113,-3.392,-10.964,-0.306,-0.589,-6.725,-3.938 | |
| 1899 | +2024-09-24,62.311,19.588,18.002,0.827,-13.164,-3.620,-10.877,-0.086,0.260,-6.569,-4.362 | |
| 1900 | +2024-09-25,62.524,19.598,17.991,0.828,-12.421,-3.384,-10.083,0.007,-0.572,-7.660,-4.304 | |
| 1901 | +2024-09-26,62.631,17.156,17.178,1.515,-12.038,-3.206,-9.495,1.911,-0.612,-7.990,-4.419 | |
| 1902 | +2024-09-27,62.557,17.191,16.802,1.410,-11.993,-3.505,-9.509,2.827,-0.658,-8.166,-4.399 | |
| 1903 | +2024-09-30,62.472,16.743,16.328,1.522,-11.672,-3.776,-8.969,1.681,-0.366,-7.564,-3.928 | |
| 1904 | +2024-10-01,62.866,15.354,15.875,0.563,-12.403,-4.454,-8.137,3.494,-1.401,-7.810,-1.080 | |
| 1905 | +2024-10-02,62.750,15.852,16.599,1.217,-11.967,-3.423,-8.936,1.931,-2.489,-8.179,-0.604 | |
| 1906 | +2024-10-03,62.684,15.685,16.532,0.334,-12.060,-4.031,-8.706,2.573,-2.020,-8.097,-0.210 | |
| 1907 | +2024-10-04,62.539,16.214,17.072,-0.293,-11.265,-4.085,-8.997,2.599,-3.066,-8.720,0.542 | |
| 1908 | +2024-10-07,62.856,16.127,17.111,-0.579,-13.275,-4.102,-8.063,2.695,-2.335,-8.836,1.257 | |
| 1909 | +2024-10-08,62.664,15.545,16.694,-0.552,-12.889,-3.594,-8.961,2.104,-0.445,-8.169,0.267 | |
| 1910 | +2024-10-09,63.103,17.102,17.418,1.031,-12.559,-2.668,-9.074,-0.614,-0.092,-11.533,0.990 | |
| 1911 | +2024-10-10,63.403,18.315,18.571,1.361,-13.955,-2.590,-9.484,-2.528,0.195,-11.473,1.589 | |
| 1912 | +2024-10-11,63.895,19.381,19.499,2.430,-13.322,-1.864,-9.707,-6.783,0.012,-11.456,1.810 | |
| 1913 | +2024-10-14,63.729,19.092,19.534,2.486,-14.236,-1.763,-9.814,-5.930,0.134,-11.028,1.525 | |
| 1914 | +2024-10-15,63.660,16.979,18.093,1.931,-13.192,-1.946,-10.435,-4.788,1.235,-7.529,-0.347 | |
| 1915 | +2024-10-16,63.691,17.752,17.958,2.418,-12.052,-3.474,-10.147,-5.591,0.582,-7.938,0.492 | |
| 1916 | +2024-10-17,63.902,17.982,17.695,2.648,-11.358,-3.212,-10.515,-5.947,0.829,-8.395,0.273 | |
| 1917 | +2024-10-18,64.094,18.337,16.843,3.128,-9.925,-3.212,-10.212,-7.933,0.741,-9.181,1.413 | |
| 1918 | +2024-10-21,64.120,18.482,17.052,3.226,-9.652,-3.132,-10.096,-8.123,0.313,-9.475,1.405 | |
| 1919 | +2024-10-22,64.061,18.357,16.734,2.572,-7.953,-3.097,-10.082,-8.473,0.129,-9.635,1.447 | |
| 1920 | +2024-10-23,64.085,18.851,17.109,3.339,-7.712,-2.788,-10.303,-8.629,-1.453,-10.138,1.724 | |
| 1921 | +2024-10-24,64.019,18.653,16.815,2.635,-7.712,-2.951,-10.536,-8.614,-0.467,-9.946,2.124 | |
| 1922 | +2024-10-25,63.965,19.065,17.266,3.176,-7.960,-2.357,-10.805,-8.844,-0.669,-9.565,0.692 | |
| 1923 | +2024-10-28,63.937,18.757,17.123,2.398,-7.280,-2.865,-10.529,-8.563,-0.989,-9.940,1.888 | |
| 1924 | +2024-10-29,63.915,20.033,18.443,2.404,-8.646,-3.017,-10.740,-7.765,-1.885,-10.595,1.769 | |
| 1925 | +2024-10-30,63.910,20.383,18.827,2.155,-8.907,-3.182,-10.610,-7.515,-1.724,-10.857,1.431 | |
| 1926 | +2024-10-31,63.993,20.342,18.794,1.975,-9.079,-2.841,-10.953,-7.338,-1.744,-10.816,1.660 | |
| 1927 | +2024-11-01,64.064,19.829,18.451,1.904,-8.617,-3.122,-10.547,-7.060,-2.251,-10.153,1.565 | |
| 1928 | +2024-11-04,64.095,20.702,18.912,2.228,-11.179,-3.147,-11.287,-6.521,-1.635,-9.537,1.465 | |
| 1929 | +2024-11-05,63.992,20.653,18.917,1.114,-10.905,-2.893,-11.645,-6.575,-1.267,-8.772,1.374 | |
| 1930 | +2024-11-06,64.249,20.446,18.962,3.156,-9.250,-0.828,-9.673,-7.181,-1.584,-10.966,-3.083 | |
| 1931 | +2024-11-07,64.229,20.627,19.404,3.365,-8.403,-0.528,-10.553,-8.584,-1.361,-11.009,-2.958 | |
| 1932 | +2024-11-08,63.975,21.394,20.210,0.668,-10.006,-1.928,-12.120,-5.782,-0.240,-11.475,-0.721 | |
| 1933 | +2024-11-11,63.976,22.280,20.744,0.291,-9.633,-1.621,-12.560,-5.356,-1.548,-11.114,-1.483 | |
| 1934 | +2024-11-12,64.059,21.704,20.472,1.013,-9.420,-1.423,-10.954,-6.113,-2.221,-10.954,-2.104 | |
| 1935 | +2024-11-13,64.340,20.854,19.789,2.268,-8.342,-0.877,-9.117,-8.046,-2.195,-10.682,-3.652 | |
| 1936 | +2024-11-14,64.174,20.164,18.873,1.987,-9.804,-1.879,-8.315,-6.536,-1.412,-10.370,-2.707 | |
| 1937 | +2024-11-15,63.630,19.229,18.860,3.272,-9.296,-0.378,-10.150,-4.621,-2.074,-10.640,-4.202 | |
| 1938 | +2024-11-18,63.878,19.447,19.265,3.730,-8.861,-0.508,-9.521,-7.070,-2.230,-10.490,-3.764 | |
| 1939 | +2024-11-19,63.884,19.132,19.102,4.291,-8.055,-1.388,-9.556,-8.942,-2.288,-10.184,-2.112 | |
| 1940 | +2024-11-20,63.520,18.396,18.524,2.658,-8.704,-1.708,-9.151,-5.625,-1.013,-9.197,-4.182 | |
| 1941 | +2024-11-21,63.621,18.620,18.758,3.457,-8.719,-3.169,-8.425,-7.889,-2.818,-9.981,0.165 | |
| 1942 | +2024-11-22,63.448,19.020,19.281,3.779,-7.984,-2.975,-8.483,-8.546,-3.433,-10.773,0.114 | |
| 1943 | +2024-11-25,63.843,19.273,19.396,5.793,-7.739,-2.209,-9.544,-11.169,-4.037,-11.210,1.447 | |
| 1944 | +2024-11-26,63.833,19.925,19.804,5.440,-7.611,-1.998,-10.348,-12.665,-3.989,-11.035,2.476 | |
| 1945 | +2024-11-27,63.454,20.074,20.585,4.393,-9.111,-3.006,-10.459,-11.293,-1.908,-10.704,1.429 | |
| 1946 | +2024-11-29,63.786,21.935,21.275,1.560,-10.317,-3.471,-11.784,-9.440,-1.260,-10.724,2.226 | |
| 1947 | +2024-12-02,63.676,21.969,21.408,1.482,-10.392,-3.327,-11.952,-9.794,-1.087,-10.826,2.520 | |
| 1948 | +2024-12-03,63.674,22.540,21.546,1.134,-11.725,-3.385,-12.201,-8.388,-0.950,-11.787,3.218 | |
| 1949 | +2024-12-04,63.805,22.264,20.868,1.719,-11.883,-3.084,-12.237,-8.406,-1.066,-11.476,3.302 | |
| 1950 | +2024-12-05,63.876,20.846,19.067,2.583,-11.300,-2.656,-10.533,-8.332,-1.576,-10.518,2.419 | |
| 1951 | +2024-12-06,63.811,22.165,20.471,1.654,-11.686,-3.048,-11.086,-8.406,-2.896,-9.840,2.672 | |
| 1952 | +2024-12-09,63.623,22.137,21.028,0.071,-13.361,-4.507,-11.076,-4.782,-2.933,-10.747,4.170 | |
| 1953 | +2024-12-10,63.751,22.137,20.873,0.035,-12.553,-4.417,-10.879,-4.432,-3.291,-11.245,3.772 | |
| 1954 | +2024-12-11,63.538,21.858,20.592,0.131,-11.367,-4.290,-11.072,-3.678,-3.484,-11.832,3.143 | |
| 1955 | +2024-12-12,63.737,21.858,20.703,0.659,-11.662,-4.605,-10.533,-5.737,-3.499,-11.511,4.327 | |
| 1956 | +2024-12-13,63.680,22.310,19.932,-0.011,-11.989,-5.464,-10.914,-4.402,-2.300,-10.979,3.817 | |
| 1957 | +2024-12-16,63.730,22.399,18.650,0.041,-11.833,-4.983,-10.769,-3.538,-2.655,-10.441,3.130 | |
| 1958 | +2024-12-17,63.804,22.584,19.483,0.003,-11.831,-4.886,-10.482,-4.667,-3.060,-10.593,3.450 | |
| 1959 | +2024-12-18,64.377,23.595,22.155,1.036,-12.408,-2.842,-9.881,-9.248,-4.945,-11.980,4.518 | |
| 1960 | +2024-12-19,64.667,24.169,21.859,1.326,-11.956,-2.300,-10.216,-8.155,-7.211,-12.774,5.258 | |
| 1961 | +2024-12-20,64.726,24.818,22.859,1.874,-12.747,-1.610,-9.808,-7.891,-8.972,-14.427,5.903 | |
| 1962 | +2024-12-23,64.438,23.434,23.431,1.374,-14.537,-2.342,-7.045,-7.155,-7.987,-13.483,4.309 | |
| 1963 | +2024-12-24,64.451,22.082,22.078,1.200,-14.184,-1.871,-4.119,-4.283,-6.491,-12.443,-1.970 | |
| 1964 | +2024-12-26,64.159,21.807,21.742,0.213,-13.775,-2.789,-4.076,-4.510,-5.556,-12.004,-1.051 | |
| 1965 | +2024-12-27,63.787,21.516,21.465,0.112,-13.619,-2.961,-4.083,-3.593,-6.384,-11.557,-0.897 | |
| 1966 | +2024-12-30,63.917,22.484,22.168,-0.221,-14.242,-2.879,-4.547,-6.235,-6.268,-11.734,1.473 | |
| 1967 | +2024-12-31,63.745,21.890,22.061,-0.425,-14.880,-3.173,-3.806,-5.588,-6.423,-11.467,1.812 | |
| 1968 | +2025-01-02,63.834,22.763,23.119,-0.376,-15.642,-3.094,-5.192,-7.610,-6.112,-10.868,3.012 | |
| 1969 | +2025-01-03,63.588,20.309,20.757,-1.226,-15.681,-3.267,-3.305,-5.278,-4.820,-9.040,1.550 | |
| 1970 | +2025-01-06,63.759,20.568,21.098,-0.123,-15.489,-2.486,-2.991,-7.166,-5.943,-9.841,2.375 | |
| 1971 | +2025-01-07,63.653,19.908,20.976,0.499,-15.789,-1.526,-2.763,-7.945,-5.611,-9.638,1.888 | |
| 1972 | +2025-01-08,63.654,20.509,21.112,0.554,-15.325,-1.404,-2.304,-8.264,-6.100,-10.359,1.581 | |
| 1973 | +2025-01-09,63.498,19.946,19.867,2.043,-14.793,-2.854,-2.040,-5.702,-7.405,-11.602,2.539 | |
| 1974 | +2025-01-10,64.387,21.777,21.412,0.074,-14.989,-1.799,-1.210,-9.845,-7.260,-12.366,4.206 | |
| 1975 | +2025-01-13,64.571,22.320,22.047,0.294,-15.029,-1.503,-0.811,-10.943,-7.965,-12.969,4.559 | |
| 1976 | +2025-01-14,64.442,21.856,22.005,-0.298,-15.333,-2.119,-1.650,-10.452,-6.918,-11.947,4.855 | |
| 1977 | +2025-01-15,64.580,22.510,22.555,-0.692,-15.839,-1.412,-2.141,-10.500,-7.633,-12.325,5.476 | |
| 1978 | +2025-01-16,64.516,23.057,22.745,-0.278,-15.528,-1.385,-2.702,-10.262,-7.629,-12.755,4.737 | |
| 1979 | +2025-01-17,64.507,23.237,22.987,-0.044,-15.591,-1.437,-3.017,-10.116,-7.429,-12.675,4.085 | |
| 1980 | +2025-01-21,64.685,23.180,23.587,-0.047,-15.602,-0.674,-2.611,-11.213,-8.291,-13.209,4.881 | |
| 1981 | +2025-01-22,64.783,22.643,22.045,-0.350,-15.434,-1.443,-2.958,-10.270,-8.235,-12.271,6.272 | |
| 1982 | +2025-01-23,64.400,21.716,21.453,-0.544,-15.813,-0.797,-1.553,-11.219,-8.072,-12.454,7.282 | |
| 1983 | +2025-01-24,64.574,22.030,21.623,-0.756,-16.100,-1.061,-1.318,-11.691,-8.998,-12.347,8.618 | |
| 1984 | +2025-01-27,64.923,21.985,21.190,1.119,-14.886,0.802,-1.137,-12.604,-9.986,-13.501,7.018 | |
| 1985 | +2025-01-28,64.885,21.817,20.627,1.593,-15.160,0.855,-0.915,-12.527,-9.819,-13.410,6.940 | |
| 1986 | +2025-01-29,64.909,22.260,21.159,1.758,-15.074,0.783,-1.380,-12.495,-10.107,-13.677,6.773 | |
| 1987 | +2025-01-30,64.791,23.027,22.268,1.585,-15.060,0.360,-2.694,-12.433,-9.687,-13.737,6.371 | |
| 1988 | +2025-01-31,64.613,23.539,22.668,1.532,-14.618,0.007,-3.626,-12.664,-9.206,-13.593,5.962 | |
| 1989 | +2025-02-03,65.352,24.467,22.909,4.502,-14.262,1.434,-4.296,-13.210,-12.603,-13.918,4.977 | |
| 1990 | +2025-02-04,65.337,24.463,22.838,4.457,-14.348,1.357,-4.791,-13.559,-12.237,-13.478,5.298 | |
| 1991 | +2025-02-05,64.810,23.365,23.126,2.611,-14.039,0.460,-3.870,-11.372,-11.937,-13.620,5.277 | |
| 1992 | +2025-02-06,64.891,23.584,23.390,2.654,-14.275,0.232,-3.849,-11.910,-11.428,-13.763,5.366 | |
| 1993 | +2025-02-07,64.707,23.257,22.440,1.839,-13.317,1.219,-4.282,-10.747,-11.868,-12.967,4.425 | |
| 1994 | +2025-02-10,64.648,22.193,21.988,1.381,-13.895,0.781,-6.694,-8.141,-10.643,-11.942,4.972 | |
| 1995 | +2025-02-11,64.826,21.767,21.273,1.406,-13.935,0.831,-5.182,-8.580,-10.795,-11.800,5.014 | |
| 1996 | +2025-02-12,65.135,22.717,22.265,1.035,-12.909,2.037,-4.779,-11.019,-11.723,-11.840,4.216 | |
| 1997 | +2025-02-13,65.068,22.300,22.561,0.538,-13.202,1.716,-5.028,-11.475,-10.706,-11.597,4.893 | |
| 1998 | +2025-02-14,64.782,23.458,23.473,-0.106,-15.833,1.077,-6.867,-11.184,-10.564,-10.670,7.217 | |
| 1999 | +2025-02-18,64.566,23.927,24.043,-0.372,-17.069,1.101,-8.003,-10.663,-10.202,-10.444,7.682 | |
| 2000 | +2025-02-19,64.738,24.340,24.413,-0.213,-17.916,1.536,-8.862,-10.837,-9.982,-10.725,8.245 | |
| 2001 | +2025-02-20,64.985,24.615,24.555,0.546,-17.007,2.055,-7.743,-11.491,-11.721,-11.680,7.871 | |
| 2002 | +2025-02-21,64.961,24.780,24.900,0.572,-16.872,2.077,-6.641,-11.281,-12.929,-12.904,8.296 | |
| 2003 | +2025-02-24,64.906,24.545,24.539,0.355,-16.969,1.828,-6.060,-11.259,-12.887,-12.380,8.288 | |
| 2004 | +2025-02-25,65.169,24.821,24.423,0.267,-16.985,1.612,-5.367,-11.926,-13.691,-11.628,8.474 | |
| 2005 | +2025-02-26,65.011,25.227,25.489,1.465,-15.932,2.688,-6.281,-12.910,-15.661,-12.564,8.478 | |
| 2006 | +2025-02-27,65.125,25.514,26.052,1.737,-15.178,2.184,-6.185,-13.086,-16.723,-13.317,9.002 | |
| 2007 | +2025-02-28,65.113,24.872,25.015,1.875,-14.933,2.254,-6.221,-13.270,-15.706,-12.447,8.560 | |
| 2008 | +2025-03-03,65.444,27.387,27.954,1.773,-14.873,1.322,-7.567,-16.860,-16.846,-13.938,11.648 | |
| 2009 | +2025-03-04,65.854,28.604,29.207,2.276,-14.940,0.207,-8.053,-16.724,-17.978,-15.224,12.626 | |
| 2010 | +2025-03-05,65.749,28.566,29.537,2.054,-14.886,0.114,-7.902,-16.045,-18.812,-15.634,13.007 | |
| 2011 | +2025-03-06,65.779,31.777,32.319,2.473,-16.155,-1.204,-8.599,-17.898,-19.778,-16.420,13.486 | |
| 2012 | +2025-03-07,65.948,32.292,32.696,3.089,-15.855,-2.441,-7.788,-17.024,-21.413,-18.414,14.859 | |
| 2013 | +2025-03-10,66.050,33.095,32.902,3.864,-15.404,-2.349,-8.176,-16.593,-22.313,-19.462,14.437 | |
| 2014 | +2025-03-11,65.889,33.722,33.670,4.016,-15.706,-3.260,-8.909,-16.187,-22.224,-19.193,14.071 | |
| 2015 | +2025-03-12,65.834,31.269,30.765,4.089,-15.601,-2.064,-7.930,-13.786,-21.099,-18.462,12.818 | |
| 2016 | +2025-03-13,65.550,31.849,31.748,5.325,-15.792,-1.596,-6.659,-13.662,-23.648,-21.712,14.146 | |
| 2017 | +2025-03-14,65.694,28.702,28.099,5.584,-15.286,0.302,-5.723,-12.758,-22.015,-19.773,12.868 | |
| 2018 | +2025-03-17,65.631,27.115,26.734,5.702,-15.183,1.670,-4.975,-12.338,-21.324,-18.772,11.370 | |
| 2019 | +2025-03-18,65.757,27.576,27.108,5.327,-15.266,1.433,-4.993,-13.813,-20.620,-18.190,11.438 | |
| 2020 | +2025-03-19,65.766,27.668,27.168,5.397,-15.057,1.241,-5.452,-13.761,-20.604,-17.974,11.373 | |
| 2021 | +2025-03-20,65.664,27.146,26.478,5.376,-15.131,1.570,-4.836,-13.100,-20.505,-17.838,10.841 | |
| 2022 | +2025-03-21,65.471,25.977,24.961,5.719,-15.136,1.948,-3.693,-11.547,-19.708,-16.984,8.463 | |
| 2023 | +2025-03-24,65.577,24.767,24.155,4.367,-13.573,1.274,-4.394,-11.111,-19.291,-16.450,10.256 | |
| 2024 | +2025-03-25,65.652,24.655,24.103,4.162,-12.890,1.638,-5.648,-10.993,-19.424,-16.688,11.083 | |
| 2025 | +2025-03-26,65.511,24.696,24.169,4.645,-13.228,1.745,-6.387,-10.969,-19.247,-16.519,11.094 | |
| 2026 | +2025-03-27,65.445,25.060,24.421,5.091,-12.745,2.089,-6.886,-11.120,-20.083,-17.047,11.220 | |
| 2027 | +2025-03-28,65.496,24.960,24.217,5.048,-12.202,2.669,-7.242,-10.891,-20.438,-17.487,11.366 | |
| 2028 | +2025-03-31,66.063,27.305,26.340,4.928,-12.215,1.759,-8.328,-12.014,-21.590,-18.323,12.137 | |
| 2029 | +2025-04-01,66.122,26.636,25.703,5.267,-12.979,2.220,-7.782,-11.426,-21.319,-18.024,11.705 | |
| 2030 | +2025-04-02,66.105,27.137,26.862,7.815,-7.665,1.008,-11.431,-12.892,-21.318,-18.623,9.106 | |
| 2031 | +2025-04-03,66.570,28.436,28.469,8.115,-8.312,-0.109,-10.764,-12.544,-22.020,-19.812,8.542 | |
| 2032 | +2025-04-04,68.556,32.214,33.039,11.065,-6.678,-2.543,-7.399,-14.120,-26.010,-25.691,6.123 | |
| 2033 | +2025-04-07,69.815,35.138,36.501,12.279,-3.551,-3.676,-7.216,-13.969,-30.110,-29.972,4.576 | |
| 2034 | +2025-04-08,69.192,33.354,34.575,10.657,-2.696,-3.556,-9.165,-15.204,-25.913,-25.965,3.913 | |
| 2035 | +2025-04-09,70.748,38.820,39.492,11.754,-5.181,-6.575,-6.223,-15.422,-30.723,-30.730,4.788 | |
| 2036 | +2025-04-10,70.154,37.798,39.391,10.556,-3.411,-7.645,-7.928,-13.564,-29.079,-29.248,3.129 | |
| 2037 | +2025-04-11,70.064,38.120,39.307,6.318,-7.494,-9.807,-8.114,-8.790,-26.767,-26.884,4.110 | |
| 2038 | +2025-04-14,69.878,37.031,37.773,3.888,-11.350,-9.909,-5.623,-4.572,-25.151,-25.074,2.986 | |
| 2039 | +2025-04-15,70.034,35.643,36.278,3.542,-12.297,-8.463,-5.354,-4.318,-23.598,-23.431,1.998 | |
| 2040 | +2025-04-16,70.144,36.287,37.198,3.371,-10.642,-9.156,-6.073,-5.871,-24.370,-23.906,3.162 | |
| 2041 | +2025-04-17,69.901,32.189,33.181,4.481,-6.216,-7.589,-9.048,-4.894,-22.130,-22.209,2.234 | |
| 2042 | +2025-04-21,69.958,31.884,33.343,4.262,-4.627,-7.379,-9.570,-5.222,-22.134,-21.984,1.428 | |
| 2043 | +2025-04-22,70.343,32.369,33.195,4.536,-1.922,-8.920,-9.002,-5.965,-22.587,-22.631,0.928 | |
| 2044 | +2025-04-23,70.219,32.515,32.846,4.506,-0.450,-10.757,-8.167,-5.595,-22.784,-22.963,0.848 | |
| 2045 | +2025-04-24,70.339,32.476,33.487,3.160,-0.608,-10.397,-11.373,-7.418,-21.723,-21.960,4.356 | |
| 2046 | +2025-04-25,70.361,32.154,33.510,2.974,-0.876,-9.956,-12.286,-7.855,-21.333,-21.710,5.378 | |
| 2047 | +2025-04-28,70.534,32.413,32.788,3.545,-0.286,-9.413,-10.674,-8.547,-21.416,-22.145,3.735 | |
| 2048 | +2025-04-29,70.394,32.234,31.360,3.254,-0.701,-8.634,-8.998,-7.388,-20.177,-22.154,1.202 | |
| 2049 | +2025-04-30,70.277,32.455,31.102,3.178,-0.296,-9.050,-8.600,-7.169,-19.932,-22.204,0.518 | |
| 2050 | +2025-05-01,69.840,31.657,28.676,3.698,-1.204,-8.411,-7.989,-5.579,-18.458,-21.219,-1.171 | |
| 2051 | +2025-05-02,69.968,31.386,28.649,3.397,-1.860,-7.586,-8.136,-6.721,-17.842,-20.888,-0.400 | |
| 2052 | +2025-05-05,69.819,30.983,28.124,3.208,-1.944,-6.180,-7.543,-6.627,-17.545,-20.457,-2.018 | |
| 2053 | +2025-05-06,69.840,29.332,26.368,4.039,-1.336,-5.902,-6.831,-6.074,-17.866,-20.859,-0.870 | |
| 2054 | +2025-05-07,69.961,28.789,26.058,3.950,-1.145,-6.095,-7.517,-5.863,-18.095,-20.488,0.406 | |
| 2055 | +2025-05-08,69.787,28.222,26.602,2.875,0.931,-8.180,-8.253,-5.233,-18.371,-20.694,2.100 | |
| 2056 | +2025-05-09,69.726,28.223,26.801,2.803,1.443,-9.315,-9.464,-3.809,-17.478,-23.084,3.879 | |
| 2057 | +2025-05-12,70.127,28.776,24.548,4.577,3.509,-6.337,-5.688,-7.259,-18.229,-22.615,-1.282 | |
| 2058 | +2025-05-13,70.245,28.782,24.897,4.755,2.057,-6.025,-5.924,-6.499,-18.380,-23.563,-0.101 | |
| 2059 | +2025-05-14,70.201,28.718,25.153,4.449,1.600,-5.986,-5.476,-6.416,-18.099,-23.705,-0.237 | |
| 2060 | +2025-05-15,70.311,29.166,26.200,4.197,3.684,-6.108,-6.072,-7.251,-18.448,-24.857,-0.511 | |
| 2061 | +2025-05-16,70.512,30.047,27.846,4.570,2.774,-6.310,-8.246,-8.504,-17.755,-26.605,2.182 | |
| 2062 | +2025-05-19,70.553,30.699,27.963,4.434,1.824,-6.302,-7.671,-8.337,-17.938,-25.546,0.875 | |
| 2063 | +2025-05-20,70.442,31.675,28.164,3.759,-1.137,-7.058,-7.241,-8.873,-16.824,-25.053,2.589 | |
| 2064 | +2025-05-21,70.493,30.872,27.438,4.842,1.703,-6.825,-8.018,-7.849,-17.454,-25.629,0.921 | |
| 2065 | +2025-05-22,70.488,31.056,27.672,5.020,2.540,-6.582,-7.710,-7.974,-17.635,-26.107,-0.280 | |
| 2066 | +2025-05-23,70.581,31.400,27.754,6.065,3.138,-6.939,-7.180,-8.425,-17.953,-26.278,-1.584 | |
| 2067 | +2025-05-27,70.523,31.410,28.130,5.659,1.782,-6.164,-6.798,-8.106,-17.169,-25.889,-2.855 | |
| 2068 | +2025-05-28,70.548,31.368,28.047,5.786,2.129,-6.145,-6.627,-8.706,-16.835,-25.578,-3.439 | |
| 2069 | +2025-05-29,70.231,31.980,28.106,3.520,0.616,-6.781,-6.421,-6.115,-16.730,-26.204,-1.971 | |
| 2070 | +2025-05-30,69.854,31.804,27.340,2.673,0.668,-7.428,-7.030,-5.000,-16.111,-26.020,-0.898 | |
| 2071 | +2025-06-02,70.002,31.908,28.434,2.291,0.543,-7.437,-7.738,-4.688,-16.098,-26.348,-0.867 | |
| 2072 | +2025-06-03,70.431,30.976,26.947,4.188,-0.153,-5.773,-4.714,-7.129,-15.025,-26.551,-2.766 | |
| 2073 | +2025-06-04,70.465,30.817,26.473,4.240,-0.952,-5.547,-4.058,-6.660,-14.330,-26.438,-3.545 | |
| 2074 | +2025-06-05,70.415,30.409,26.966,3.938,0.745,-7.368,-4.095,-6.141,-15.144,-25.183,-4.126 | |
| 2075 | +2025-06-06,70.387,29.920,26.275,4.153,0.084,-6.439,-3.761,-6.065,-14.526,-25.640,-4.000 | |
| 2076 | +2025-06-09,70.588,29.411,26.227,3.753,-1.240,-6.163,-3.236,-5.452,-14.363,-25.530,-3.406 | |
| 2077 | +2025-06-10,70.401,29.349,25.222,3.614,-0.746,-6.631,-2.513,-5.725,-14.168,-25.854,-2.550 | |
| 2078 | +2025-06-11,70.250,29.182,24.216,4.152,-0.693,-5.263,-2.886,-5.861,-14.350,-25.608,-2.890 | |
| 2079 | +2025-06-12,70.343,29.047,23.528,3.876,0.600,-5.083,-3.977,-4.815,-14.303,-25.158,-3.714 | |
| 2080 | +2025-06-13,70.268,29.711,24.020,4.081,-0.294,-4.786,-3.247,-5.953,-14.710,-25.261,-3.562 | |
| 2081 | +2025-06-16,70.359,29.260,23.868,5.007,0.604,-3.510,-1.893,-7.896,-15.020,-26.548,-3.871 | |
| 2082 | +2025-06-17,70.306,30.448,25.794,4.069,-0.088,-5.561,-0.908,-10.362,-13.366,-25.848,-4.179 | |
| 2083 | +2025-06-18,70.115,30.561,25.717,3.463,-1.949,-6.014,-1.758,-9.654,-12.160,-25.055,-3.150 | |
| 2084 | +2025-06-20,69.667,30.276,25.752,3.496,-3.909,-5.735,-1.007,-8.593,-11.436,-24.405,-4.440 | |
| 2085 | +2025-06-23,69.756,30.794,26.643,2.268,-6.275,-7.142,-2.679,-6.563,-10.722,-23.727,-2.596 | |
| 2086 | +2025-06-24,69.654,30.554,25.801,2.663,-5.776,-6.696,-2.473,-6.828,-10.262,-23.591,-3.393 | |
| 2087 | +2025-06-25,70.062,32.906,29.356,3.679,-6.959,-5.463,-1.074,-12.266,-9.795,-24.630,-5.753 | |
| 2088 | +2025-06-26,69.737,33.989,30.069,3.903,-8.979,-5.212,-1.338,-12.200,-10.115,-24.686,-5.431 | |
| 2089 | +2025-06-27,70.122,33.883,30.054,5.120,-8.133,-3.888,-0.746,-12.260,-11.632,-26.716,-5.681 | |
| 2090 | +2025-06-30,70.363,32.497,29.022,5.928,-9.841,-2.955,0.332,-12.013,-10.389,-26.348,-6.233 | |
| 2091 | +2025-07-01,70.328,32.457,28.423,5.920,-8.525,-2.646,-0.929,-12.889,-9.648,-26.191,-5.972 | |
| 2092 | +2025-07-02,70.015,32.172,27.445,5.824,-12.581,-3.294,1.810,-11.454,-6.974,-25.145,-7.804 | |
| 2093 | +2025-07-03,69.860,32.875,28.838,6.024,-10.158,-4.782,0.430,-12.568,-9.615,-26.522,-4.523 | |
| 2094 | +2025-07-07,69.967,32.751,28.840,5.812,-8.969,-5.106,0.673,-12.425,-9.269,-26.352,-5.955 | |
| 2095 | +2025-07-08,70.007,32.183,29.037,5.326,-8.497,-5.348,0.748,-12.333,-8.430,-26.225,-6.460 | |
| 2096 | +2025-07-09,70.077,31.708,28.741,4.907,-8.758,-5.933,1.452,-11.999,-7.522,-26.012,-6.586 | |
| 2097 | +2025-07-10,69.821,31.986,28.895,4.656,-8.384,-6.615,0.950,-11.495,-7.660,-25.052,-7.281 | |
| 2098 | +2025-07-11,69.913,31.930,28.824,4.839,-7.994,-6.718,0.576,-11.209,-7.570,-24.947,-7.732 | |
| 2099 | +2025-07-14,69.956,31.917,28.934,4.445,-8.403,-7.168,1.158,-11.286,-7.583,-24.923,-7.091 | |
| 2100 | +2025-07-15,69.707,32.215,29.211,2.567,-9.780,-8.046,2.215,-11.188,-7.393,-24.378,-5.423 | |
| 2101 | +2025-07-16,69.562,32.256,27.991,2.757,-10.337,-7.559,3.362,-11.716,-8.565,-23.796,-4.393 | |
| 2102 | +2025-07-17,69.632,33.173,30.544,1.064,-11.345,-8.456,2.979,-10.933,-7.697,-24.411,-4.918 | |
| 2103 | +2025-07-18,69.622,34.529,31.871,1.962,-11.977,-8.491,1.655,-11.127,-7.986,-26.153,-4.282 | |
| 2104 | +2025-07-21,69.410,35.095,33.494,0.086,-12.357,-9.728,3.243,-12.194,-8.187,-25.715,-3.736 | |
| 2105 | +2025-07-22,69.130,34.788,32.909,-0.892,-9.987,-9.704,0.719,-11.740,-7.405,-24.353,-4.336 | |
| 2106 | +2025-07-23,69.130,34.730,32.885,-1.393,-8.971,-10.403,0.094,-11.543,-6.789,-23.990,-4.621 | |
| 2107 | +2025-07-24,69.198,35.206,33.514,-1.753,-9.129,-10.275,0.285,-12.059,-6.902,-24.721,-4.165 | |
| 2108 | +2025-07-25,69.339,36.156,34.683,-2.351,-11.729,-11.164,1.383,-12.190,-7.261,-24.943,-2.584 | |
| 2109 | +2025-07-28,69.184,36.501,33.968,-1.380,-11.604,-10.639,0.318,-11.700,-7.099,-24.715,-3.650 | |
| 2110 | +2025-07-29,67.314,38.979,34.720,0.516,-13.163,-11.730,-3.039,-9.939,-4.599,-23.830,-7.916 | |
| 2111 | +2025-07-30,67.574,38.319,34.235,0.106,-11.527,-11.647,-3.973,-10.853,-4.796,-24.298,-5.567 | |
| 2112 | +2025-07-31,67.727,38.594,34.496,-2.405,-10.090,-12.889,-4.786,-11.591,-4.750,-23.789,-2.789 | |
| 2113 | +2025-08-01,68.101,39.525,34.979,-2.267,-9.539,-12.917,-5.760,-11.432,-6.613,-25.316,-0.660 | |
| 2114 | +2025-08-04,68.084,40.427,36.107,-4.291,-9.653,-14.078,-4.562,-12.871,-5.012,-23.770,-2.297 | |
| 2115 | +2025-08-05,68.279,41.210,36.917,-5.394,-10.144,-14.773,-3.004,-13.795,-4.271,-23.483,-3.262 | |
| 2116 | +2025-08-06,68.154,41.246,37.037,-5.643,-10.476,-15.053,-3.318,-14.186,-3.949,-23.066,-2.593 | |
| 2117 | +2025-08-07,68.056,41.648,37.259,-5.488,-10.161,-14.776,-5.034,-14.332,-4.200,-22.717,-2.200 | |
| 2118 | +2025-08-08,67.890,41.348,37.422,-4.572,-9.628,-14.211,-7.974,-14.678,-2.587,-22.709,-2.411 | |
| 2119 | +2025-08-11,67.979,41.337,37.190,-4.463,-10.039,-14.170,-7.213,-15.103,-2.836,-22.192,-2.511 | |
| 2120 | +2025-08-12,67.977,41.422,36.804,-5.045,-9.809,-14.223,-6.431,-15.720,-2.926,-21.899,-2.174 | |
| 2121 | +2025-08-13,68.145,42.159,38.306,-5.590,-9.774,-15.062,-7.274,-14.936,-3.089,-21.836,-2.904 | |
| 2122 | +2025-08-14,68.060,41.511,37.630,-5.850,-9.460,-14.999,-7.920,-15.397,-2.059,-20.768,-2.688 | |
| 2123 | +2025-08-15,68.243,41.520,37.460,-5.178,-9.124,-14.457,-6.702,-15.048,-3.243,-22.404,-2.824 | |
| 2124 | +2025-08-18,68.456,41.367,37.249,-5.424,-9.630,-14.303,-6.381,-14.371,-2.791,-22.408,-3.308 | |
| 2125 | +2025-08-19,68.246,41.491,37.058,-5.691,-9.181,-13.529,-5.476,-16.050,-2.677,-23.165,-2.779 | |
| 2126 | +2025-08-20,68.175,41.361,37.187,-5.924,-8.905,-13.246,-5.955,-16.326,-3.152,-22.715,-2.324 | |
| 2127 | +2025-08-21,68.181,42.109,37.878,-5.532,-8.819,-13.226,-6.261,-16.748,-4.177,-23.114,-2.110 | |
| 2128 | +2025-08-22,68.198,42.740,39.118,-5.585,-9.249,-13.186,-8.053,-17.436,-4.710,-22.179,-1.460 | |
| 2129 | +2025-08-25,68.165,42.133,38.168,-6.019,-9.811,-13.161,-6.674,-15.141,-4.914,-22.158,-2.422 | |
| 2130 | +2025-08-26,68.210,42.186,38.207,-5.824,-9.733,-13.313,-6.636,-15.338,-4.800,-22.213,-2.536 | |
| 2131 | +2025-08-27,68.440,42.659,38.100,-5.140,-9.213,-12.439,-5.968,-16.629,-4.897,-22.967,-3.508 | |
| 2132 | +2025-08-28,68.501,42.405,37.036,-5.495,-9.075,-12.177,-4.032,-17.240,-3.680,-24.396,-3.346 | |
| 2133 | +2025-08-29,68.376,42.846,37.626,-5.012,-9.635,-11.381,-4.029,-17.582,-4.816,-23.789,-4.228 | |
| 2134 | +2025-09-02,68.385,43.054,38.343,-5.878,-9.934,-11.524,-5.495,-18.169,-4.793,-23.753,-1.850 | |
| 2135 | +2025-09-03,68.442,42.925,38.363,-6.304,-9.696,-11.712,-5.987,-18.683,-3.422,-23.881,-1.605 | |
| 2136 | +2025-09-04,68.456,42.734,37.833,-4.814,-10.011,-11.562,-6.230,-19.588,-2.305,-23.205,-2.853 | |
| 2137 | +2025-09-05,68.589,42.529,37.937,-5.441,-10.086,-12.088,-4.751,-19.056,-3.014,-23.744,-2.288 | |
| 2138 | +2025-09-08,69.077,41.088,37.072,-6.305,-8.710,-12.486,-6.477,-18.541,-0.674,-22.105,-2.863 | |
| 2139 | +2025-09-09,69.188,41.321,37.109,-6.288,-8.304,-12.556,-6.371,-18.568,-0.738,-22.751,-2.855 | |
| 2140 | +2025-09-10,69.185,41.862,37.335,-5.652,-8.965,-12.332,-6.923,-18.301,-1.355,-22.751,-2.919 | |
| 2141 | +2025-09-11,69.057,43.143,39.091,-4.601,-11.408,-12.482,-8.261,-17.912,-2.055,-22.834,-2.682 | |
| 2142 | +2025-09-12,69.621,43.545,40.193,-7.624,-9.557,-12.615,-8.585,-18.717,-1.208,-24.134,-1.298 | |
| 2143 | +2025-09-15,70.023,43.108,40.066,-9.529,-6.477,-12.660,-8.014,-19.509,-1.327,-24.868,-0.790 | |
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| 2266 | +2026-03-11,71.073,28.391,29.584,10.869,-3.284,1.438,4.339,-15.005,-12.108,-22.832,-21.393 | |
added
results/rev_rolling_w500.csv
+2016 −0
@@ -0,0 +1,2016 @@ | ||
| 1 | +date,TSI,NET_ES,NET_NQ,NET_EURUSD,NET_USDJPY,NET_GBPUSD,NET_GC,NET_CL,NET_BTC,NET_ETH,NET_VIX | |
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| 1766 | +2025-03-13,58.673,19.548,13.897,4.770,-12.826,-2.239,-5.237,-6.264,-9.393,-2.442,0.187 | |
| 1767 | +2025-03-14,58.684,18.931,13.292,4.539,-12.750,-1.831,-5.224,-6.193,-9.023,-2.231,0.491 | |
| 1768 | +2025-03-17,58.474,18.100,12.988,3.858,-12.956,-1.662,-5.251,-4.801,-8.665,-1.599,-0.013 | |
| 1769 | +2025-03-18,58.522,18.483,13.178,4.118,-12.924,-1.875,-5.177,-5.233,-8.796,-1.931,0.158 | |
| 1770 | +2025-03-19,58.507,18.720,13.289,4.279,-12.719,-2.127,-5.242,-5.321,-8.914,-2.234,0.270 | |
| 1771 | +2025-03-20,58.494,18.670,13.222,4.191,-12.721,-2.164,-5.044,-5.318,-8.819,-2.352,0.334 | |
| 1772 | +2025-03-21,58.462,18.240,12.903,3.965,-12.818,-1.934,-4.923,-4.701,-8.707,-2.295,0.269 | |
| 1773 | +2025-03-24,58.463,17.860,12.542,3.978,-12.645,-1.762,-4.764,-4.587,-8.479,-2.267,0.125 | |
| 1774 | +2025-03-25,58.328,17.729,12.668,3.569,-12.932,-1.699,-5.551,-3.965,-8.661,-2.063,0.904 | |
| 1775 | +2025-03-26,58.234,17.695,12.761,3.591,-13.038,-1.756,-6.081,-3.953,-8.322,-2.088,1.192 | |
| 1776 | +2025-03-27,58.222,17.783,12.800,3.708,-12.815,-1.656,-6.126,-4.288,-8.359,-2.023,0.975 | |
| 1777 | +2025-03-28,58.186,17.970,13.087,3.858,-12.564,-1.640,-5.810,-4.269,-8.925,-2.238,0.531 | |
| 1778 | +2025-03-31,58.356,18.743,13.758,4.083,-12.242,-2.226,-6.093,-5.121,-9.159,-2.216,0.472 | |
| 1779 | +2025-04-01,58.271,18.607,13.734,4.209,-12.296,-2.079,-6.133,-4.919,-9.184,-2.346,0.407 | |
| 1780 | +2025-04-02,58.636,20.087,14.612,4.241,-11.978,-3.211,-5.640,-6.428,-9.690,-2.369,0.376 | |
| 1781 | +2025-04-03,59.000,20.685,15.383,5.251,-12.247,-3.627,-4.690,-7.227,-10.027,-2.555,-0.946 | |
| 1782 | +2025-04-04,60.170,22.046,16.824,7.095,-12.594,-4.884,-3.805,-8.963,-10.101,-3.137,-2.482 | |
| 1783 | +2025-04-07,61.389,24.621,19.104,9.155,-12.182,-5.618,-1.046,-10.603,-13.473,-6.285,-3.672 | |
| 1784 | +2025-04-08,61.149,23.938,18.476,8.924,-11.487,-5.572,-1.259,-10.318,-12.767,-5.671,-4.265 | |
| 1785 | +2025-04-09,62.426,27.601,21.981,9.816,-12.927,-7.655,0.487,-11.680,-15.487,-8.087,-4.050 | |
| 1786 | +2025-04-10,62.167,27.189,21.614,9.274,-12.547,-8.551,0.004,-9.962,-14.570,-7.199,-5.252 | |
| 1787 | +2025-04-11,61.894,26.993,21.715,7.326,-13.729,-9.451,-1.070,-8.217,-12.989,-5.728,-4.849 | |
| 1788 | +2025-04-14,61.618,26.205,20.908,6.438,-13.806,-9.094,-0.951,-5.966,-12.830,-5.586,-5.318 | |
| 1789 | +2025-04-15,61.469,26.168,20.759,5.847,-13.691,-9.050,-1.514,-5.015,-12.248,-5.130,-6.127 | |
| 1790 | +2025-04-16,61.530,26.841,21.325,5.971,-13.250,-9.604,-1.111,-6.193,-12.723,-5.057,-6.198 | |
| 1791 | +2025-04-17,61.388,26.113,20.630,5.706,-13.137,-8.835,-2.060,-5.224,-11.966,-4.509,-6.717 | |
| 1792 | +2025-04-21,61.435,26.024,20.532,5.952,-12.841,-8.829,-1.740,-5.412,-11.955,-4.959,-6.772 | |
| 1793 | +2025-04-22,61.558,26.164,20.286,6.869,-12.887,-9.312,-0.427,-5.352,-12.888,-5.417,-7.036 | |
| 1794 | +2025-04-23,61.695,26.428,20.742,7.668,-12.684,-9.952,0.849,-6.516,-13.076,-5.772,-7.686 | |
| 1795 | +2025-04-24,61.533,26.344,21.938,6.369,-12.922,-9.275,-2.511,-7.496,-11.592,-4.597,-6.259 | |
| 1796 | +2025-04-25,61.586,26.209,22.362,5.917,-13.100,-8.659,-3.328,-7.720,-11.288,-4.714,-5.679 | |
| 1797 | +2025-04-28,61.603,26.042,21.673,6.123,-13.042,-8.959,-3.533,-7.450,-11.075,-4.366,-5.414 | |
| 1798 | +2025-04-29,61.508,25.637,20.586,6.743,-12.688,-9.405,-3.319,-7.388,-10.843,-4.443,-4.881 | |
| 1799 | +2025-04-30,61.482,25.824,20.571,7.167,-12.519,-9.761,-3.106,-8.033,-10.660,-4.427,-5.058 | |
| 1800 | +2025-05-01,61.474,26.082,21.475,7.181,-12.867,-9.548,-2.603,-8.221,-10.734,-4.294,-6.471 | |
| 1801 | +2025-05-02,61.464,25.953,21.332,7.052,-12.968,-9.333,-2.765,-8.617,-10.407,-4.231,-6.016 | |
| 1802 | +2025-05-05,61.457,25.863,21.217,6.777,-12.944,-9.096,-2.836,-8.629,-10.475,-4.119,-5.759 | |
| 1803 | +2025-05-06,61.312,25.258,19.967,6.674,-12.499,-9.613,-2.709,-7.908,-10.381,-4.197,-4.591 | |
| 1804 | +2025-05-07,61.302,25.112,19.841,6.640,-12.581,-9.536,-3.007,-7.775,-10.100,-3.946,-4.648 | |
| 1805 | +2025-05-08,61.313,25.196,19.825,6.764,-12.366,-9.781,-2.673,-7.734,-10.453,-4.491,-4.289 | |
| 1806 | +2025-05-09,61.238,25.137,20.218,6.376,-12.406,-10.138,-3.095,-6.840,-10.588,-4.942,-3.723 | |
| 1807 | +2025-05-12,61.528,25.330,20.186,7.162,-12.437,-9.852,-2.046,-8.425,-10.443,-4.425,-5.049 | |
| 1808 | +2025-05-13,61.494,25.003,20.472,6.605,-12.956,-9.825,-2.700,-7.438,-10.060,-4.834,-4.268 | |
| 1809 | +2025-05-14,61.457,24.937,20.467,6.700,-12.771,-9.756,-2.717,-7.737,-9.810,-5.181,-4.131 | |
| 1810 | +2025-05-15,61.440,24.804,20.892,6.838,-12.694,-9.884,-2.572,-7.462,-9.882,-5.317,-4.724 | |
| 1811 | +2025-05-16,61.510,25.117,21.352,6.532,-13.185,-9.735,-3.346,-7.945,-9.414,-5.340,-4.037 | |
| 1812 | +2025-05-19,61.505,25.285,21.352,6.679,-12.930,-9.631,-3.129,-8.117,-9.757,-5.666,-4.087 | |
| 1813 | +2025-05-20,61.413,25.242,21.270,6.683,-13.310,-9.945,-2.943,-7.565,-9.570,-5.569,-4.293 | |
| 1814 | +2025-05-21,61.412,25.264,21.255,6.761,-13.372,-10.080,-2.978,-7.503,-9.696,-5.424,-4.228 | |
| 1815 | +2025-05-22,61.411,25.220,21.230,6.626,-13.236,-9.957,-2.993,-7.231,-9.791,-5.559,-4.310 | |
| 1816 | +2025-05-23,61.395,25.087,21.057,6.864,-13.293,-10.554,-2.966,-6.801,-9.719,-5.886,-3.789 | |
| 1817 | +2025-05-27,61.284,25.131,21.193,6.784,-13.617,-10.202,-2.987,-6.645,-9.359,-5.384,-4.915 | |
| 1818 | +2025-05-28,61.271,25.129,21.308,6.679,-13.623,-10.246,-2.921,-6.540,-9.169,-5.398,-5.219 | |
| 1819 | +2025-05-29,61.269,25.028,21.419,6.555,-13.748,-10.250,-2.987,-6.402,-8.910,-5.373,-5.332 | |
| 1820 | +2025-05-30,61.345,25.007,21.356,6.517,-13.649,-10.450,-3.123,-6.613,-8.471,-5.431,-5.144 | |
| 1821 | +2025-06-02,61.296,24.889,21.489,6.307,-13.900,-10.394,-2.998,-5.969,-8.222,-5.624,-5.577 | |
| 1822 | +2025-06-03,61.606,25.362,22.138,6.636,-14.032,-9.933,-2.592,-7.156,-8.119,-5.855,-6.449 | |
| 1823 | +2025-06-04,61.577,25.364,22.030,6.677,-14.000,-9.880,-2.585,-6.758,-8.036,-5.976,-6.835 | |
| 1824 | +2025-06-05,61.493,25.189,21.809,6.458,-13.550,-9.884,-2.920,-7.340,-8.371,-5.716,-5.675 | |
| 1825 | +2025-06-06,61.539,25.153,21.795,6.362,-13.692,-9.774,-2.916,-7.133,-8.148,-6.000,-5.646 | |
| 1826 | +2025-06-09,61.634,25.409,22.357,6.239,-13.793,-9.653,-3.087,-6.921,-7.977,-6.094,-6.479 | |
| 1827 | +2025-06-10,61.614,25.381,22.051,6.365,-13.855,-9.739,-3.024,-6.874,-7.939,-6.235,-6.130 | |
| 1828 | +2025-06-11,61.578,25.153,21.713,6.317,-13.389,-9.100,-3.194,-6.501,-8.442,-6.082,-6.475 | |
| 1829 | +2025-06-12,61.710,24.869,21.116,6.666,-12.798,-9.155,-3.267,-5.791,-8.610,-6.046,-6.985 | |
| 1830 | +2025-06-13,61.687,25.021,21.067,7.023,-12.528,-9.191,-3.257,-6.186,-8.803,-6.044,-7.102 | |
| 1831 | +2025-06-16,61.583,25.325,21.186,6.888,-12.268,-9.038,-3.076,-7.232,-8.491,-6.318,-6.977 | |
| 1832 | +2025-06-17,61.711,25.638,21.769,7.150,-11.994,-8.848,-2.885,-8.682,-8.489,-6.431,-7.229 | |
| 1833 | +2025-06-18,61.728,25.588,21.485,7.004,-11.969,-8.833,-3.189,-8.920,-8.355,-6.454,-6.357 | |
| 1834 | +2025-06-20,61.797,25.640,21.705,7.006,-11.541,-8.674,-2.426,-9.361,-8.361,-6.611,-7.377 | |
| 1835 | +2025-06-23,61.828,25.251,21.597,6.479,-12.581,-9.307,-3.084,-6.853,-8.382,-6.454,-6.666 | |
| 1836 | +2025-06-24,61.733,25.771,21.790,6.732,-12.648,-8.903,-3.136,-7.656,-7.718,-6.048,-8.184 | |
| 1837 | +2025-06-25,62.119,27.586,23.972,7.103,-12.493,-8.201,-3.004,-11.318,-7.489,-6.407,-9.749 | |
| 1838 | +2025-06-26,62.044,28.438,24.525,6.712,-12.314,-8.255,-3.027,-12.314,-7.337,-6.229,-10.200 | |
| 1839 | +2025-06-27,62.071,29.020,24.978,6.422,-12.622,-8.076,-3.236,-12.757,-7.067,-6.358,-10.303 | |
| 1840 | +2025-06-30,62.091,29.054,25.122,6.640,-12.672,-8.193,-3.323,-12.915,-7.068,-6.717,-9.927 | |
| 1841 | +2025-07-01,61.999,28.967,25.003,6.643,-12.228,-7.937,-3.455,-13.074,-6.985,-7.524,-9.409 | |
| 1842 | +2025-07-02,61.978,28.956,25.003,6.543,-12.402,-8.506,-3.099,-12.966,-6.889,-7.531,-9.108 | |
| 1843 | +2025-07-03,62.027,29.334,25.083,6.286,-12.638,-8.627,-2.917,-13.030,-7.055,-7.391,-9.045 | |
| 1844 | +2025-07-07,62.067,29.124,24.865,6.678,-12.597,-8.320,-2.919,-13.117,-6.916,-7.362,-9.437 | |
| 1845 | +2025-07-08,62.100,29.356,25.299,6.191,-13.066,-8.678,-3.165,-12.817,-6.630,-7.474,-9.016 | |
| 1846 | +2025-07-09,62.092,29.014,25.293,6.086,-13.056,-8.853,-3.248,-12.060,-6.630,-7.390,-9.155 | |
| 1847 | +2025-07-10,62.119,29.085,25.505,6.062,-12.811,-8.550,-3.361,-12.102,-6.831,-7.315,-9.681 | |
| 1848 | +2025-07-11,62.132,29.173,25.752,6.069,-12.959,-8.513,-3.370,-12.122,-6.904,-7.308,-9.816 | |
| 1849 | +2025-07-14,62.166,29.205,26.077,5.879,-12.934,-8.522,-3.544,-12.106,-6.785,-7.433,-9.836 | |
| 1850 | +2025-07-15,62.161,29.016,25.308,5.732,-12.962,-8.535,-3.659,-12.012,-6.727,-7.029,-9.132 | |
| 1851 | +2025-07-16,62.247,28.757,24.861,6.569,-12.369,-8.207,-3.559,-12.730,-7.132,-7.214,-8.976 | |
| 1852 | +2025-07-17,62.258,29.322,25.800,5.429,-12.757,-8.661,-3.714,-12.103,-6.961,-7.425,-8.930 | |
| 1853 | +2025-07-18,62.410,29.717,26.149,4.360,-13.443,-9.102,-3.990,-11.558,-6.349,-7.646,-8.139 | |
| 1854 | +2025-07-21,62.635,30.153,26.908,4.080,-14.032,-9.011,-3.328,-11.975,-6.341,-8.285,-8.169 | |
| 1855 | +2025-07-22,62.417,30.012,26.876,4.426,-11.977,-9.038,-4.046,-12.105,-6.797,-8.727,-8.624 | |
| 1856 | +2025-07-23,62.404,29.970,26.867,4.455,-11.975,-8.957,-4.225,-12.193,-6.906,-8.611,-8.426 | |
| 1857 | +2025-07-24,62.429,29.828,26.711,4.445,-11.979,-8.949,-4.106,-12.140,-6.840,-8.890,-8.081 | |
| 1858 | +2025-07-25,62.626,30.344,27.520,3.921,-12.653,-9.191,-3.828,-12.425,-6.871,-9.473,-7.345 | |
| 1859 | +2025-07-28,62.680,30.508,27.762,4.083,-12.575,-8.987,-3.791,-12.651,-7.187,-10.172,-6.990 | |
| 1860 | +2025-07-29,62.581,30.558,27.804,4.564,-12.433,-8.654,-4.128,-12.944,-7.600,-10.711,-6.456 | |
| 1861 | +2025-07-30,62.566,30.118,27.160,5.140,-12.365,-8.401,-4.335,-12.753,-7.651,-10.607,-6.305 | |
| 1862 | +2025-07-31,62.534,30.213,27.109,5.162,-12.142,-8.381,-4.505,-12.787,-7.735,-11.021,-5.914 | |
| 1863 | +2025-08-01,62.724,30.542,27.130,5.199,-11.779,-8.376,-4.943,-12.837,-8.204,-11.671,-5.061 | |
| 1864 | +2025-08-04,62.663,30.995,27.718,5.613,-12.028,-8.205,-5.302,-12.823,-8.301,-12.566,-5.102 | |
| 1865 | +2025-08-05,62.735,31.263,27.978,5.637,-12.157,-8.238,-5.132,-12.930,-8.379,-12.727,-5.315 | |
| 1866 | +2025-08-06,62.733,31.272,28.016,5.591,-12.126,-8.352,-5.130,-12.760,-8.315,-12.999,-5.194 | |
| 1867 | +2025-08-07,62.581,31.557,28.249,5.688,-12.096,-8.094,-5.995,-12.981,-8.725,-13.202,-4.400 | |
| 1868 | +2025-08-08,62.547,31.429,28.146,5.776,-12.095,-7.995,-5.854,-13.090,-7.793,-13.560,-4.965 | |
| 1869 | +2025-08-11,62.578,31.621,28.390,5.936,-12.090,-7.787,-6.370,-13.362,-7.891,-13.426,-5.022 | |
| 1870 | +2025-08-12,62.391,31.979,28.562,5.224,-12.131,-8.039,-7.273,-14.124,-7.141,-12.829,-4.228 | |
| 1871 | +2025-08-13,62.415,32.186,29.066,4.726,-12.202,-8.258,-7.389,-13.671,-7.132,-12.566,-4.760 | |
| 1872 | +2025-08-14,62.367,31.530,28.317,4.882,-12.214,-8.565,-7.291,-14.038,-6.282,-11.872,-4.468 | |
| 1873 | +2025-08-15,62.540,31.852,28.731,5.063,-12.423,-8.286,-6.984,-13.853,-6.728,-12.673,-4.699 | |
| 1874 | +2025-08-18,62.552,31.768,28.567,5.197,-12.445,-8.205,-6.721,-13.587,-6.808,-13.026,-4.741 | |
| 1875 | +2025-08-19,62.489,32.496,29.524,4.963,-12.663,-7.829,-7.137,-13.933,-7.156,-13.309,-4.954 | |
| 1876 | +2025-08-20,62.488,32.317,29.220,4.829,-12.789,-8.152,-7.167,-13.947,-6.583,-13.285,-4.443 | |
| 1877 | +2025-08-21,62.579,32.296,29.174,5.025,-12.795,-8.092,-7.162,-14.053,-6.530,-13.273,-4.590 | |
| 1878 | +2025-08-22,62.557,32.824,30.184,4.956,-12.572,-7.614,-8.788,-15.199,-6.432,-12.540,-4.819 | |
| 1879 | +2025-08-25,62.563,32.615,29.587,4.539,-13.078,-8.048,-7.953,-13.887,-6.690,-12.464,-4.620 | |
| 1880 | +2025-08-26,62.610,32.569,29.462,4.369,-13.146,-8.252,-7.912,-13.106,-6.743,-13.013,-4.229 | |
| 1881 | +2025-08-27,62.699,32.698,29.579,4.326,-13.053,-8.039,-7.539,-12.903,-6.957,-13.604,-4.509 | |
| 1882 | +2025-08-28,62.721,32.581,29.436,4.135,-12.962,-7.937,-7.311,-12.862,-6.806,-13.741,-4.532 | |
| 1883 | +2025-08-29,62.741,32.959,30.046,4.048,-12.999,-7.779,-7.457,-13.493,-6.921,-14.091,-4.314 | |
| 1884 | +2025-09-02,62.785,33.159,30.623,3.694,-13.030,-7.863,-8.031,-13.960,-7.159,-13.791,-3.641 | |
| 1885 | +2025-09-03,62.779,33.194,30.711,3.756,-12.603,-7.726,-8.357,-14.353,-6.881,-14.013,-3.728 | |
| 1886 | +2025-09-04,62.791,33.419,30.681,4.041,-12.322,-8.024,-9.206,-14.372,-6.645,-13.832,-3.741 | |
| 1887 | +2025-09-05,62.856,33.166,30.621,4.205,-12.373,-7.881,-8.805,-14.594,-6.773,-13.837,-3.729 | |
| 1888 | +2025-09-08,62.907,33.260,30.713,4.189,-12.492,-7.748,-9.772,-14.089,-6.296,-13.910,-3.853 | |
| 1889 | +2025-09-09,62.832,33.356,30.811,4.494,-12.446,-7.418,-10.058,-14.426,-6.402,-14.083,-3.828 | |
| 1890 | +2025-09-10,62.827,33.437,30.904,4.534,-12.401,-7.349,-10.472,-14.523,-6.276,-14.070,-3.784 | |
| 1891 | +2025-09-11,62.866,33.630,31.299,3.928,-12.387,-7.418,-10.261,-14.499,-6.129,-14.209,-3.953 | |
| 1892 | +2025-09-12,63.096,33.963,32.010,3.149,-12.900,-7.900,-10.490,-14.132,-5.975,-14.424,-3.301 | |
| 1893 | +2025-09-15,63.322,34.329,32.626,3.217,-13.252,-8.031,-10.635,-14.013,-6.474,-14.880,-2.885 | |
| 1894 | +2025-09-16,63.438,34.399,32.866,3.273,-13.294,-7.776,-10.518,-13.977,-6.507,-15.216,-3.251 | |
| 1895 | +2025-09-17,63.503,34.515,32.005,4.516,-12.516,-7.102,-10.226,-15.530,-7.536,-15.574,-2.552 | |
| 1896 | +2025-09-18,63.495,33.806,31.534,4.718,-12.256,-6.858,-10.022,-15.427,-6.760,-15.195,-3.540 | |
| 1897 | +2025-09-19,63.517,33.593,31.823,4.326,-12.747,-7.442,-9.942,-15.407,-5.755,-14.422,-4.027 | |
| 1898 | +2025-09-22,63.585,33.815,32.528,4.039,-13.463,-7.841,-10.122,-15.247,-5.482,-14.259,-3.967 | |
| 1899 | +2025-09-23,63.609,33.751,32.600,4.104,-13.272,-8.004,-10.044,-15.222,-5.390,-14.254,-4.269 | |
| 1900 | +2025-09-24,63.723,33.775,32.740,4.137,-12.899,-8.140,-10.114,-14.872,-5.653,-14.657,-4.316 | |
| 1901 | +2025-09-25,63.788,33.974,32.784,3.965,-12.934,-8.219,-9.418,-15.430,-6.137,-14.795,-3.789 | |
| 1902 | +2025-09-26,63.811,33.914,32.744,4.009,-12.809,-8.289,-9.518,-14.951,-6.209,-15.172,-3.719 | |
| 1903 | +2025-09-29,63.808,33.187,32.002,4.134,-12.217,-8.473,-9.093,-15.514,-5.654,-14.649,-3.723 | |
| 1904 | +2025-09-30,63.828,33.603,32.490,4.064,-12.977,-8.294,-9.579,-15.401,-6.116,-15.004,-2.785 | |
| 1905 | +2025-10-01,63.761,33.908,32.793,4.210,-13.254,-8.026,-9.952,-15.379,-6.779,-15.421,-2.098 | |
| 1906 | +2025-10-02,63.813,34.218,33.157,4.038,-13.283,-8.184,-10.106,-15.865,-6.467,-15.270,-2.239 | |
| 1907 | +2025-10-03,63.952,34.499,33.508,3.828,-13.408,-8.142,-10.496,-16.021,-6.641,-15.307,-1.820 | |
| 1908 | +2025-10-06,63.979,34.001,33.162,3.692,-13.327,-7.971,-9.817,-15.814,-6.536,-15.218,-2.172 | |
| 1909 | +2025-10-07,64.053,33.351,32.519,3.652,-12.998,-7.941,-9.524,-15.631,-5.659,-14.910,-2.859 | |
| 1910 | +2025-10-08,64.100,33.849,32.882,3.742,-12.924,-7.703,-10.680,-15.905,-5.302,-15.602,-2.357 | |
| 1911 | +2025-10-09,64.142,33.612,32.535,3.753,-13.473,-7.656,-9.837,-15.873,-5.155,-15.992,-1.914 | |
| 1912 | +2025-10-10,64.715,32.241,30.442,3.432,-12.603,-6.950,-7.127,-15.570,-5.119,-15.589,-3.157 | |
| 1913 | +2025-10-13,64.694,32.200,30.565,3.352,-12.292,-6.966,-7.390,-15.384,-5.100,-15.147,-3.836 | |
| 1914 | +2025-10-14,64.813,31.511,29.915,3.169,-12.102,-7.216,-7.103,-15.470,-4.518,-14.268,-3.918 | |
| 1915 | +2025-10-15,64.774,31.410,29.837,3.448,-11.573,-7.019,-7.915,-15.134,-4.490,-13.938,-4.625 | |
| 1916 | +2025-10-16,64.971,31.192,29.495,2.901,-12.019,-7.074,-6.580,-15.162,-4.544,-14.316,-3.893 | |
| 1917 | +2025-10-17,64.939,31.118,29.441,2.275,-12.032,-7.304,-5.797,-15.376,-4.518,-14.510,-3.297 | |
| 1918 | +2025-10-20,64.899,31.397,29.846,3.472,-11.350,-6.629,-8.082,-15.801,-4.717,-14.263,-3.873 | |
| 1919 | +2025-10-21,64.776,31.162,29.536,3.271,-10.500,-6.772,-7.771,-16.002,-4.891,-14.363,-3.670 | |
| 1920 | +2025-10-22,64.734,30.499,28.722,3.094,-10.773,-6.561,-6.167,-15.751,-5.008,-14.379,-3.676 | |
| 1921 | +2025-10-23,64.728,30.715,28.864,3.497,-10.280,-6.729,-7.221,-16.452,-4.835,-14.108,-3.451 | |
| 1922 | +2025-10-24,64.655,31.685,29.831,2.585,-10.467,-6.426,-8.616,-16.440,-4.551,-14.026,-3.577 | |
| 1923 | +2025-10-27,64.675,31.988,30.282,1.972,-10.089,-6.990,-9.141,-16.818,-4.220,-14.007,-2.977 | |
| 1924 | +2025-10-28,64.493,32.133,30.367,2.110,-10.962,-6.542,-8.852,-16.074,-4.555,-14.443,-3.182 | |
| 1925 | +2025-10-29,64.699,30.640,28.367,2.614,-10.034,-5.060,-6.686,-16.098,-5.131,-14.492,-4.120 | |
| 1926 | +2025-10-30,64.769,30.620,28.121,2.642,-9.734,-4.937,-6.208,-16.326,-5.193,-14.568,-4.416 | |
| 1927 | +2025-10-31,64.856,30.434,27.921,2.729,-9.535,-4.961,-6.202,-16.114,-5.645,-14.209,-4.419 | |
| 1928 | +2025-11-03,64.922,30.868,28.225,2.891,-10.427,-4.824,-6.594,-15.870,-5.637,-14.204,-4.428 | |
| 1929 | +2025-11-04,64.911,30.782,27.988,2.719,-10.528,-4.934,-6.296,-16.072,-5.436,-13.989,-4.234 | |
| 1930 | +2025-11-05,64.657,30.038,27.726,2.451,-9.148,-4.834,-5.667,-15.339,-5.119,-14.336,-5.771 | |
| 1931 | +2025-11-06,64.748,30.232,27.732,2.406,-9.202,-4.917,-5.962,-15.548,-4.759,-14.270,-5.712 | |
| 1932 | +2025-11-07,64.744,30.088,27.545,2.634,-9.037,-4.978,-5.915,-15.355,-4.746,-14.254,-5.982 | |
| 1933 | +2025-11-10,64.767,29.941,27.119,2.843,-8.494,-4.746,-6.226,-15.013,-4.581,-14.542,-6.300 | |
| 1934 | +2025-11-11,64.766,29.887,26.921,3.069,-8.142,-5.003,-6.380,-14.794,-4.597,-14.751,-6.211 | |
| 1935 | +2025-11-12,64.743,29.972,26.989,2.835,-8.087,-4.769,-6.292,-14.976,-4.665,-14.641,-6.366 | |
| 1936 | +2025-11-13,64.862,30.241,27.691,2.138,-9.042,-4.668,-5.149,-15.546,-4.906,-14.246,-6.513 | |
| 1937 | +2025-11-14,64.663,30.004,27.965,1.822,-9.349,-3.699,-5.041,-13.770,-5.403,-14.072,-8.457 | |
| 1938 | +2025-11-17,64.636,29.906,27.684,1.946,-9.023,-4.053,-4.896,-14.003,-5.296,-13.914,-8.351 | |
| 1939 | +2025-11-18,64.733,30.386,28.499,1.474,-9.604,-4.247,-4.364,-14.835,-5.167,-13.633,-8.509 | |
| 1940 | +2025-11-19,64.783,30.625,28.820,1.223,-9.807,-4.366,-4.291,-15.267,-5.034,-13.475,-8.427 | |
| 1941 | +2025-11-20,65.133,31.079,29.597,0.729,-10.291,-4.615,-3.653,-16.334,-4.975,-13.525,-8.012 | |
| 1942 | +2025-11-21,65.281,31.383,30.111,0.464,-10.607,-4.449,-3.516,-16.388,-5.494,-13.928,-7.577 | |
| 1943 | +2025-11-24,65.299,31.178,29.337,0.917,-9.893,-4.088,-3.590,-16.682,-5.572,-13.886,-7.720 | |
| 1944 | +2025-11-25,65.318,31.401,29.528,0.744,-10.060,-4.012,-4.015,-17.141,-5.570,-13.668,-7.207 | |
| 1945 | +2025-11-26,65.249,31.888,30.325,0.670,-10.159,-5.658,-3.491,-17.130,-5.106,-13.837,-7.501 | |
| 1946 | +2025-11-28,65.375,32.494,31.383,0.302,-8.677,-6.809,-3.126,-17.493,-4.646,-13.962,-9.467 | |
| 1947 | +2025-12-01,65.421,31.710,30.442,0.199,-9.398,-6.086,-3.296,-17.939,-4.508,-13.776,-7.349 | |
| 1948 | +2025-12-02,65.480,31.680,30.416,0.385,-9.306,-5.890,-3.206,-17.882,-4.579,-14.011,-7.607 | |
| 1949 | +2025-12-03,65.532,31.761,30.353,0.447,-9.470,-5.689,-3.305,-17.994,-4.704,-13.908,-7.490 | |
| 1950 | +2025-12-04,65.580,31.925,30.372,0.412,-9.611,-5.920,-3.154,-17.987,-4.833,-14.036,-7.168 | |
| 1951 | +2025-12-05,65.623,31.935,30.184,0.615,-9.399,-5.659,-3.095,-18.126,-4.847,-14.170,-7.438 | |
| 1952 | +2025-12-08,65.669,32.180,30.519,0.323,-9.767,-5.941,-3.259,-17.575,-4.796,-14.561,-7.124 | |
| 1953 | +2025-12-09,65.782,32.418,30.640,0.334,-9.357,-5.988,-3.133,-17.453,-4.928,-15.114,-7.420 | |
| 1954 | +2025-12-10,65.841,31.857,29.829,0.882,-8.389,-5.154,-2.959,-17.700,-4.914,-15.079,-8.372 | |
| 1955 | +2025-12-11,65.873,32.210,29.822,0.765,-8.580,-5.355,-2.911,-17.959,-4.987,-14.924,-8.081 | |
| 1956 | +2025-12-12,65.778,32.238,30.044,0.708,-8.700,-5.555,-2.781,-17.894,-4.950,-14.932,-8.179 | |
| 1957 | +2025-12-15,65.798,32.276,29.897,0.825,-8.785,-5.361,-2.706,-17.843,-5.167,-14.909,-8.227 | |
| 1958 | +2025-12-16,65.803,32.442,29.680,0.630,-8.752,-5.062,-2.654,-17.943,-5.438,-15.098,-7.805 | |
| 1959 | +2025-12-17,65.813,32.526,30.029,0.610,-8.760,-5.256,-2.415,-18.364,-5.479,-15.047,-7.845 | |
| 1960 | +2025-12-18,65.921,32.541,29.995,0.664,-8.595,-5.105,-2.759,-18.406,-5.642,-15.084,-7.608 | |
| 1961 | +2025-12-19,65.946,32.673,30.420,0.875,-8.773,-5.226,-2.838,-18.274,-6.035,-15.349,-7.472 | |
| 1962 | +2025-12-22,65.862,33.083,31.516,1.169,-9.709,-5.490,-2.179,-18.782,-6.847,-15.143,-7.616 | |
| 1963 | +2025-12-23,65.762,33.856,32.457,1.247,-10.383,-5.727,-2.010,-19.275,-7.749,-14.884,-7.533 | |
| 1964 | +2025-12-24,66.156,35.009,33.485,0.846,-11.167,-6.151,-3.681,-18.982,-7.152,-15.100,-7.106 | |
| 1965 | +2025-12-26,66.115,35.139,33.660,1.003,-11.068,-6.180,-3.434,-18.965,-7.528,-15.447,-7.179 | |
| 1966 | +2025-12-29,65.987,34.025,32.396,1.557,-11.045,-5.938,-2.229,-18.627,-7.852,-15.658,-6.630 | |
| 1967 | +2025-12-30,66.044,34.668,33.402,1.203,-11.357,-6.231,-2.861,-19.129,-7.923,-15.288,-6.485 | |
| 1968 | +2025-12-31,66.075,34.894,33.796,1.031,-11.399,-6.348,-3.443,-18.850,-7.856,-14.993,-6.832 | |
| 1969 | +2026-01-02,66.000,35.227,34.394,1.128,-11.816,-6.322,-3.395,-19.201,-8.620,-15.364,-6.031 | |
| 1970 | +2026-01-05,65.906,34.798,34.321,1.244,-11.922,-6.287,-3.135,-19.104,-8.808,-15.282,-5.824 | |
| 1971 | +2026-01-06,65.838,34.833,34.616,1.142,-12.120,-6.426,-3.144,-19.418,-8.848,-15.158,-5.477 | |
| 1972 | +2026-01-07,66.006,35.377,34.969,0.972,-11.861,-6.296,-3.309,-20.289,-8.894,-15.619,-5.049 | |
| 1973 | +2026-01-08,66.006,35.477,34.780,1.115,-11.956,-6.046,-3.218,-20.476,-9.059,-15.969,-4.649 | |
| 1974 | +2026-01-09,66.002,35.594,34.862,1.089,-12.093,-5.974,-3.547,-20.222,-8.977,-16.167,-4.566 | |
| 1975 | +2026-01-12,65.928,35.182,34.846,1.117,-12.152,-5.901,-3.047,-20.050,-9.153,-16.126,-4.717 | |
| 1976 | +2026-01-13,65.958,35.138,34.831,1.001,-12.280,-6.006,-3.138,-19.857,-9.293,-16.176,-4.219 | |
| 1977 | +2026-01-14,65.718,34.998,34.895,0.224,-12.916,-6.987,-2.566,-18.899,-9.342,-16.031,-3.376 | |
| 1978 | +2026-01-15,65.890,35.300,34.687,1.310,-12.056,-5.675,-3.268,-21.050,-8.912,-15.978,-4.357 | |
| 1979 | +2026-01-16,65.930,35.575,34.754,1.733,-11.697,-5.124,-3.447,-22.020,-9.009,-16.101,-4.665 | |
| 1980 | +2026-01-19,66.150,35.641,34.726,2.003,-11.208,-4.468,-4.315,-22.382,-8.992,-16.124,-4.882 | |
| 1981 | +2026-01-20,66.147,35.509,34.722,2.291,-12.246,-4.750,-4.373,-22.419,-8.952,-15.954,-3.829 | |
| 1982 | +2026-01-21,66.100,35.658,34.739,2.391,-12.985,-4.930,-4.038,-23.171,-8.980,-15.678,-3.006 | |
| 1983 | +2026-01-22,66.150,35.926,34.961,2.657,-12.157,-5.491,-4.714,-22.948,-9.017,-15.833,-3.384 | |
| 1984 | +2026-01-23,66.159,36.033,35.009,3.193,-12.853,-5.158,-5.073,-22.966,-8.966,-15.893,-3.326 | |
| 1985 | +2026-01-26,65.997,36.077,34.683,3.690,-12.653,-4.850,-5.004,-22.646,-9.277,-16.580,-3.439 | |
| 1986 | +2026-01-27,65.655,36.087,34.863,3.126,-12.290,-4.950,-4.756,-22.356,-9.239,-16.795,-3.689 | |
| 1987 | +2026-01-28,65.621,34.432,33.565,5.285,-11.141,-3.718,-3.807,-22.063,-9.550,-17.795,-5.208 | |
| 1988 | +2026-01-29,65.460,33.606,32.985,6.346,-10.549,-3.160,-2.019,-22.274,-9.890,-18.609,-6.435 | |
| 1989 | +2026-01-30,65.554,32.376,31.949,7.206,-10.194,-2.851,1.515,-21.862,-10.686,-19.970,-7.484 | |
| 1990 | +2026-02-02,65.367,32.180,31.781,7.204,-9.722,-2.677,2.364,-21.915,-11.100,-20.563,-7.550 | |
| 1991 | +2026-02-03,65.346,32.064,32.148,6.690,-8.778,-3.316,2.721,-22.430,-10.989,-20.416,-7.695 | |
| 1992 | +2026-02-04,65.399,31.943,31.839,6.860,-8.891,-2.853,2.793,-22.698,-11.022,-20.608,-7.362 | |
| 1993 | +2026-02-05,65.372,31.693,31.619,6.818,-9.025,-2.821,3.196,-22.304,-11.086,-20.850,-7.237 | |
| 1994 | +2026-02-06,65.355,31.874,31.491,7.124,-7.783,-2.809,2.356,-22.701,-11.576,-21.128,-6.849 | |
| 1995 | +2026-02-09,65.376,32.625,32.033,6.951,-8.427,-3.090,1.362,-22.480,-12.097,-21.146,-5.731 | |
| 1996 | +2026-02-10,65.441,33.038,32.301,6.636,-8.470,-3.251,0.744,-22.455,-12.099,-21.160,-5.284 | |
| 1997 | +2026-02-11,65.620,32.369,31.934,7.773,-7.990,-2.589,1.064,-22.816,-12.448,-21.248,-6.050 | |
| 1998 | +2026-02-12,65.622,32.427,32.219,8.184,-8.479,-2.290,0.797,-23.072,-12.572,-21.238,-5.976 | |
| 1999 | +2026-02-13,65.573,32.519,32.427,8.045,-9.300,-2.231,0.771,-22.784,-12.335,-21.170,-5.944 | |
| 2000 | +2026-02-17,65.645,32.651,32.578,7.831,-9.643,-2.061,1.216,-23.066,-12.539,-21.331,-5.635 | |
| 2001 | +2026-02-18,65.850,32.664,32.667,8.216,-9.764,-1.637,0.522,-22.805,-12.676,-21.332,-5.855 | |
| 2002 | +2026-02-19,65.830,32.614,32.739,8.466,-9.019,-1.595,1.422,-23.339,-13.785,-22.064,-5.441 | |
| 2003 | +2026-02-20,65.871,32.525,32.647,8.351,-9.090,-1.656,1.776,-23.522,-13.667,-21.893,-5.470 | |
| 2004 | +2026-02-23,65.965,32.716,32.715,8.526,-8.967,-1.491,1.370,-23.599,-13.798,-21.918,-5.553 | |
| 2005 | +2026-02-24,65.928,33.303,33.511,9.076,-8.071,-1.012,0.996,-24.599,-15.403,-22.711,-5.091 | |
| 2006 | +2026-02-25,65.907,33.495,33.730,9.742,-7.813,-0.613,0.527,-24.612,-16.096,-23.109,-5.251 | |
| 2007 | +2026-02-26,65.924,33.395,33.620,9.552,-7.786,-0.572,0.641,-24.901,-15.736,-22.900,-5.312 | |
| 2008 | +2026-02-27,65.859,33.679,33.999,9.620,-7.947,-0.186,0.641,-25.934,-15.886,-22.899,-5.087 | |
| 2009 | +2026-03-02,66.115,33.493,33.704,9.122,-8.997,-0.017,1.001,-24.255,-16.370,-23.123,-4.560 | |
| 2010 | +2026-03-03,66.457,32.795,32.863,9.445,-10.475,0.818,2.112,-22.030,-17.307,-24.110,-4.110 | |
| 2011 | +2026-03-04,66.239,33.162,32.975,8.360,-11.059,0.498,2.474,-21.824,-16.403,-23.635,-4.548 | |
| 2012 | +2026-03-05,66.440,32.903,32.741,8.621,-11.959,0.427,3.013,-20.621,-16.920,-24.229,-3.977 | |
| 2013 | +2026-03-06,66.519,32.994,32.712,8.550,-12.343,0.540,3.154,-20.354,-16.885,-24.358,-4.011 | |
| 2014 | +2026-03-09,66.452,32.873,32.200,8.838,-14.056,0.245,2.761,-17.968,-17.110,-24.669,-3.114 | |
| 2015 | +2026-03-10,66.345,33.020,32.329,8.925,-13.315,0.605,2.753,-18.940,-17.406,-24.657,-3.314 | |
| 2016 | +2026-03-11,66.176,32.950,32.713,10.555,-12.412,2.204,3.375,-21.410,-19.128,-26.011,-2.835 | |
added
results/rev_table_connectedness_full.csv
+13 −0
@@ -0,0 +1,13 @@ | ||
| 1 | +,ES,NQ,EURUSD,USDJPY,GBPUSD,GC,CL,BTC,ETH,VIX,FROM | |
| 2 | +ES,31.86,28.27,5.37,4.83,4.23,6.14,5.45,1.26,0.65,11.94,68.14 | |
| 3 | +NQ,30.05,33.69,4.70,4.28,3.73,5.76,4.84,1.11,0.51,11.32,66.31 | |
| 4 | +EURUSD,9.13,7.97,35.48,14.35,16.49,9.97,3.90,0.37,0.35,2.00,64.52 | |
| 5 | +USDJPY,8.46,7.52,15.17,44.54,9.09,8.98,3.48,0.35,0.29,2.12,55.46 | |
| 6 | +GBPUSD,8.92,7.52,19.33,10.19,40.11,7.12,3.54,0.61,0.84,1.83,59.89 | |
| 7 | +GC,10.95,9.41,11.42,9.77,6.35,41.36,5.65,0.55,0.58,3.96,58.64 | |
| 8 | +CL,12.18,10.35,3.95,3.83,2.79,6.77,53.94,0.79,0.90,4.51,46.06 | |
| 9 | +BTC,1.77,1.49,0.35,0.20,0.47,0.44,0.42,66.67,27.05,1.12,33.33 | |
| 10 | +ETH,1.38,0.91,0.57,0.28,1.11,1.36,0.77,27.95,64.92,0.75,35.08 | |
| 11 | +VIX,21.23,18.45,3.27,2.52,2.39,4.86,3.77,2.08,1.53,39.90,60.10 | |
| 12 | +TO,104.09,91.90,64.14,50.24,46.64,51.41,31.82,35.05,32.68,39.55,54.75 | |
| 13 | +NET,35.95,25.58,-0.39,-5.22,-13.24,-7.23,-14.23,1.72,-2.39,-20.55, | |
added
results/rev_table_connectedness_full_ci.csv
+12 −0
@@ -0,0 +1,12 @@ | ||
| 1 | +,TO,TO_lo,TO_hi,FROM,FROM_lo,FROM_hi,NET,NET_lo,NET_hi | |
| 2 | +ES,104.09,98.33,109.10,68.14,66.66,69.79,35.95,29.85,41.54 | |
| 3 | +NQ,91.90,86.17,96.89,66.31,64.80,68.18,25.58,19.04,31.27 | |
| 4 | +EURUSD,64.14,58.65,70.55,64.52,62.23,66.97,-0.39,-6.02,5.80 | |
| 5 | +USDJPY,50.24,45.38,56.02,55.46,52.46,58.91,-5.22,-10.17,0.17 | |
| 6 | +GBPUSD,46.64,41.73,52.83,59.89,56.70,63.13,-13.24,-18.00,-7.45 | |
| 7 | +GC,51.41,45.96,58.25,58.64,55.78,61.60,-7.23,-12.50,-0.79 | |
| 8 | +CL,31.82,26.14,37.71,46.06,40.52,52.38,-14.23,-21.57,-6.65 | |
| 9 | +BTC,35.05,31.54,39.62,33.33,30.46,37.79,1.72,-3.35,6.35 | |
| 10 | +ETH,32.68,28.97,37.44,35.08,31.97,39.79,-2.39,-7.95,2.13 | |
| 11 | +VIX,39.55,34.62,46.17,60.10,57.67,62.69,-20.55,-25.21,-13.96 | |
| 12 | +TSI,,,,,,,54.75,53.15,56.89 | |
added
results/rev_table_granger.csv
+17 −0
@@ -0,0 +1,17 @@ | ||
| 1 | +Cause,Effect,T,F,p_F,Wald_HAC,p_HAC,sum_coef | |
| 2 | +ES,VIX,2510,19.9354,0.0000,62.7846,0.0000,0.0072 | |
| 3 | +NQ,VIX,2510,14.4025,0.0000,48.8836,0.0000,0.0082 | |
| 4 | +VIX,ES,2510,5.3337,0.0003,22.2121,0.0002,-0.0674 | |
| 5 | +VIX,NQ,2510,5.8289,0.0001,22.1837,0.0002,-0.0614 | |
| 6 | +ES,NQ,2510,1.1026,0.3536,4.8399,0.3041,0.0166 | |
| 7 | +NQ,ES,2510,0.6216,0.6471,2.0186,0.7323,0.0356 | |
| 8 | +ES,BTC,2510,1.3273,0.2574,6.2935,0.1783,-0.0293 | |
| 9 | +NQ,BTC,2510,1.1656,0.3240,4.7706,0.3117,-0.0308 | |
| 10 | +VIX,BTC,2510,0.6002,0.6625,2.3196,0.6772,-0.0073 | |
| 11 | +BTC,ES,2510,2.3330,0.0536,11.2099,0.0243,-0.0078 | |
| 12 | +BTC,NQ,2510,1.4718,0.2081,6.6522,0.1555,-0.0083 | |
| 13 | +BTC,VIX,2510,5.1000,0.0004,24.4647,0.0001,0.0313 | |
| 14 | +USDJPY,ES,2510,3.4956,0.0075,13.6906,0.0084,-0.0357 | |
| 15 | +ES,USDJPY,2510,1.5900,0.1742,5.7726,0.2168,-0.0117 | |
| 16 | +GC,BTC,2510,3.8011,0.0044,15.3177,0.0041,-0.0625 | |
| 17 | +BTC,GC,2510,6.4364,0.0000,33.0835,0.0000,-0.0241 | |
added
results/rev_table_lag_selection.csv
+12 −0
@@ -0,0 +1,12 @@ | ||
| 1 | +p,AIC,BIC,HQ | |
| 2 | +0,-21.840,-21.817,-21.832 | |
| 3 | +1,-30.424,-30.168,-30.331 | |
| 4 | +2,-31.159,-30.670,-30.981 | |
| 5 | +3,-31.448,-30.727,-31.186 | |
| 6 | +4,-31.575,-30.622,-31.229 | |
| 7 | +5,-31.626,-30.440,-31.195 | |
| 8 | +6,-31.620,-30.201,-31.105 | |
| 9 | +7,-31.602,-29.950,-31.002 | |
| 10 | +8,-31.598,-29.714,-30.914 | |
| 11 | +9,-31.584,-29.467,-30.815 | |
| 12 | +10,-31.573,-29.223,-30.720 | |
added
results/rev_table_regime_covid_crash.csv
+13 −0
@@ -0,0 +1,13 @@ | ||
| 1 | +,ES,NQ,EURUSD,USDJPY,GBPUSD,GC,CL,BTC,ETH,VIX,FROM | |
| 2 | +ES,20.16,20.40,9.76,18.53,8.44,8.14,2.24,5.30,2.38,4.65,79.84 | |
| 3 | +NQ,18.92,21.03,9.29,18.44,7.37,8.19,2.73,6.12,3.06,4.84,78.97 | |
| 4 | +EURUSD,10.43,11.85,20.25,23.00,13.52,9.03,2.40,5.35,3.17,1.01,79.75 | |
| 5 | +USDJPY,10.39,11.14,12.94,36.84,10.28,7.76,0.65,5.45,3.44,1.11,63.16 | |
| 6 | +GBPUSD,11.21,11.91,13.86,17.45,22.19,9.37,2.38,7.49,3.28,0.84,77.81 | |
| 7 | +GC,12.06,13.33,9.35,16.04,6.33,22.47,4.97,8.77,5.43,1.27,77.53 | |
| 8 | +CL,8.12,9.01,4.05,2.28,2.04,20.77,47.64,1.87,3.06,1.15,52.36 | |
| 9 | +BTC,7.96,10.18,7.60,15.42,5.90,7.92,4.28,24.88,13.86,2.01,75.12 | |
| 10 | +ETH,5.19,7.79,6.54,15.82,4.67,4.55,1.89,18.09,33.44,2.02,66.56 | |
| 11 | +VIX,15.01,16.65,7.11,17.98,3.24,0.49,1.80,2.30,0.96,34.46,65.54 | |
| 12 | +TO,99.28,112.25,80.49,144.97,61.78,76.20,23.35,60.74,38.65,18.91,71.66 | |
| 13 | +NET,19.44,33.28,0.74,81.81,-16.02,-1.33,-29.00,-14.38,-27.91,-46.63, | |
added
results/rev_table_regime_precovid.csv
+13 −0
@@ -0,0 +1,13 @@ | ||
| 1 | +,ES,NQ,EURUSD,USDJPY,GBPUSD,GC,CL,BTC,ETH,VIX,FROM | |
| 2 | +ES,26.89,27.08,3.21,14.15,0.66,5.60,6.02,0.68,0.12,15.59,73.11 | |
| 3 | +NQ,26.16,28.98,3.17,13.56,0.58,5.41,6.42,0.84,0.09,14.80,71.02 | |
| 4 | +EURUSD,11.78,12.27,31.56,11.98,11.13,10.05,5.06,0.23,0.43,5.50,68.44 | |
| 5 | +USDJPY,18.55,19.29,7.33,23.86,2.02,10.59,6.74,1.10,0.39,10.13,76.14 | |
| 6 | +GBPUSD,8.46,7.12,13.54,5.94,49.02,4.85,2.42,0.81,2.04,5.80,50.98 | |
| 7 | +GC,11.12,11.99,7.33,16.33,1.63,31.24,6.77,5.39,2.57,5.62,68.76 | |
| 8 | +CL,15.90,18.66,1.71,12.50,1.21,6.00,32.47,3.24,1.54,6.78,67.53 | |
| 9 | +BTC,1.27,1.03,3.78,0.58,1.34,1.90,2.04,74.46,12.99,0.61,25.54 | |
| 10 | +ETH,0.77,0.72,1.28,0.63,2.54,0.60,0.81,24.59,67.47,0.58,32.53 | |
| 11 | +VIX,20.37,19.90,2.30,9.73,0.91,5.27,3.93,1.42,0.96,35.19,64.81 | |
| 12 | +TO,114.40,118.06,43.66,85.41,22.01,50.27,40.21,38.29,21.14,65.41,59.89 | |
| 13 | +NET,41.29,47.04,-24.78,9.27,-28.97,-18.49,-27.32,12.75,-11.39,0.60, | |
added
results/rev_table_regime_rate_hikes.csv
+13 −0
@@ -0,0 +1,13 @@ | ||
| 1 | +,ES,NQ,EURUSD,USDJPY,GBPUSD,GC,CL,BTC,ETH,VIX,FROM | |
| 2 | +ES,29.18,23.64,8.09,1.97,7.55,9.44,3.16,3.36,3.38,10.23,70.82 | |
| 3 | +NQ,27.23,27.61,7.40,2.17,7.15,9.10,2.87,3.40,3.68,9.39,72.39 | |
| 4 | +EURUSD,10.08,8.22,28.66,7.82,20.66,11.73,4.51,2.14,2.33,3.86,71.34 | |
| 5 | +USDJPY,3.90,3.54,12.86,46.30,13.34,8.60,3.51,3.15,3.06,1.73,53.70 | |
| 6 | +GBPUSD,9.10,6.49,19.05,9.42,36.52,10.69,2.27,1.61,1.58,3.27,63.48 | |
| 7 | +GC,12.16,9.75,10.79,5.31,9.49,26.79,7.21,5.93,5.79,6.78,73.21 | |
| 8 | +CL,6.62,4.08,6.39,2.54,2.96,14.59,45.40,4.77,4.78,7.87,54.60 | |
| 9 | +BTC,7.01,5.99,2.06,1.53,2.14,5.62,2.51,35.83,33.20,4.12,64.17 | |
| 10 | +ETH,6.80,5.95,1.93,1.53,2.02,5.43,2.95,31.65,38.81,2.94,61.19 | |
| 11 | +VIX,13.33,11.03,6.66,2.86,7.16,6.82,4.05,4.80,4.15,39.14,60.86 | |
| 12 | +TO,96.23,78.68,75.23,35.14,72.47,82.02,33.05,60.81,61.95,50.19,64.58 | |
| 13 | +NET,25.41,6.29,3.89,-18.56,8.99,8.81,-21.55,-3.37,0.76,-10.67, | |
added
results/rev_table_regime_spotetf_era.csv
+13 −0
@@ -0,0 +1,13 @@ | ||
| 1 | +,ES,NQ,EURUSD,USDJPY,GBPUSD,GC,CL,BTC,ETH,VIX,FROM | |
| 2 | +ES,25.04,24.05,6.98,4.84,6.52,6.23,3.83,4.66,3.47,14.38,74.96 | |
| 3 | +NQ,24.45,26.12,6.00,4.89,5.95,5.69,3.76,5.32,3.93,13.90,73.88 | |
| 4 | +EURUSD,10.21,9.01,31.50,11.69,19.47,7.38,3.56,1.14,1.41,4.63,68.50 | |
| 5 | +USDJPY,9.32,10.50,13.31,37.57,11.49,5.08,3.59,1.91,2.04,5.19,62.43 | |
| 6 | +GBPUSD,10.30,9.59,21.35,10.26,27.36,8.14,4.32,1.80,1.89,4.98,72.64 | |
| 7 | +GC,7.74,6.87,11.03,6.14,9.55,44.97,5.07,2.42,1.93,4.28,55.03 | |
| 8 | +CL,8.56,8.80,6.43,3.65,4.63,8.86,47.84,2.35,1.63,7.25,52.16 | |
| 9 | +BTC,7.47,7.87,2.02,1.79,3.09,4.86,2.82,40.12,24.66,5.30,59.88 | |
| 10 | +ETH,6.97,7.17,4.22,3.80,4.50,6.22,1.60,24.21,35.81,5.50,64.19 | |
| 11 | +VIX,19.32,18.69,6.04,4.07,5.61,6.63,3.69,3.64,3.75,28.56,71.44 | |
| 12 | +TO,104.33,102.55,77.37,51.14,70.82,59.09,32.23,47.46,44.71,65.40,65.51 | |
| 13 | +NET,29.37,28.67,8.86,-11.29,-1.81,4.06,-19.93,-12.42,-19.47,-6.04, | |
added
results/rev_table_regimes.csv
+5 −0
@@ -0,0 +1,5 @@ | ||
| 1 | +Regime,T,p,TSI,TSI_lo,TSI_hi,NET_ES,NET_ES_lo,NET_ES_hi,NET_NQ,NET_NQ_lo,NET_NQ_hi,NET_EURUSD,NET_EURUSD_lo,NET_EURUSD_hi,NET_USDJPY,NET_USDJPY_lo,NET_USDJPY_hi,NET_GBPUSD,NET_GBPUSD_lo,NET_GBPUSD_hi,NET_GC,NET_GC_lo,NET_GC_hi,NET_CL,NET_CL_lo,NET_CL_hi,NET_BTC,NET_BTC_lo,NET_BTC_hi,NET_ETH,NET_ETH_lo,NET_ETH_hi,NET_VIX,NET_VIX_lo,NET_VIX_hi,TSI_var4,NET_USDJPY_var4,NET_BTC_var4 | |
| 2 | +Pre-COVID (2019-01 to 2020-02),292,4,59.89,58.90,65.71,41.29,23.03,55.64,47.04,26.40,60.52,-24.78,-35.56,-3.33,9.27,-5.73,30.09,-28.97,-42.46,-7.71,-18.49,-32.39,2.23,-27.32,-40.28,-3.29,12.75,-14.84,24.05,-11.39,-27.14,1.73,0.60,-19.21,23.08,,, | |
| 3 | +COVID crash (2020-03 to 2020-06),85,1,71.66,65.86,78.13,19.44,-23.31,52.14,33.28,-12.74,63.50,0.74,-29.05,37.30,81.81,7.31,135.29,-16.02,-41.67,27.40,-1.33,-38.03,39.40,-29.00,-52.09,12.03,-14.38,-45.86,32.90,-27.91,-54.20,19.06,-46.63,-61.37,-11.20,71.36,105.34,-4.62 | |
| 4 | +Rate hikes (2022-01 to 2022-12),254,4,64.58,63.67,70.54,25.41,8.21,36.66,6.29,-6.92,18.77,3.89,-7.47,18.38,-18.56,-29.17,-4.08,8.99,-3.82,20.76,8.81,-3.62,22.26,-21.55,-33.50,-4.97,-3.37,-16.67,12.36,0.76,-12.00,14.27,-10.67,-24.11,4.56,,, | |
| 5 | +Spot-ETF era (2024-01 to 2026-03),544,4,65.51,63.36,69.32,29.37,18.43,37.91,28.67,16.28,37.55,8.86,-2.42,19.43,-11.29,-22.54,0.83,-1.81,-12.25,10.01,4.06,-9.48,16.95,-19.93,-31.38,-4.64,-12.42,-20.36,-2.08,-19.47,-27.69,-9.20,-6.04,-17.33,8.72,,, | |
added
results/rev_table_robustness.csv
+16 −0
@@ -0,0 +1,16 @@ | ||
| 1 | +Specification,T,p,H,TSI,NET_ES,NET_NQ,NET_USDJPY,NET_GC,NET_CL,NET_BTC,NET_ETH,NET_VIX,Own_BTC | |
| 2 | +"Baseline: log RV, trading days, VAR(4), H = 10",2514,4,10,54.75,35.95,25.58,-5.22,-7.23,-14.23,1.72,-2.39,-20.55,66.67 | |
| 3 | +RV in levels (trading days),2514,4,10,50.04,41.61,29.84,-8.01,-4.77,-15.62,1.62,-1.59,-23.36,74.77 | |
| 4 | +VAR(1),2514,1,10,53.66,38.60,26.18,-5.37,-11.85,-5.81,7.42,-3.97,-27.39,69.75 | |
| 5 | +VAR(2),2514,2,10,54.13,36.58,25.86,-4.88,-8.82,-7.32,3.53,-3.36,-26.06,69.47 | |
| 6 | +VAR(3),2514,3,10,54.88,36.03,25.53,-5.09,-7.24,-9.98,2.67,-2.99,-24.23,68.33 | |
| 7 | +VAR(6),2514,6,10,55.48,35.04,23.74,-5.64,-5.17,-14.85,1.34,-3.83,-16.66,65.27 | |
| 8 | +H = 5,2514,4,5,54.44,32.47,22.69,-5.73,-7.11,-11.94,-0.31,-2.72,-17.05,66.07 | |
| 9 | +H = 20,2514,4,20,55.33,39.78,28.83,-5.37,-7.40,-17.43,4.44,-2.39,-23.28,67.34 | |
| 10 | +Weekend-inclusive crypto RV,2514,4,10,54.89,36.27,25.98,-5.14,-7.35,-14.63,0.35,-1.22,-20.87,65.74 | |
| 11 | +Sample 2018-01 to 2026-03,2063,4,10,57.40,35.71,27.68,-7.72,-5.70,-17.26,3.30,-5.62,-19.00,61.58 | |
| 12 | +Sample 2016-03 to 2019-12,954,4,10,51.52,35.81,23.90,9.94,-13.21,-8.94,3.01,-6.56,-14.41,77.65 | |
| 13 | +Sample 2020-01 to 2026-03,1560,4,10,60.88,36.40,28.16,-11.31,-1.79,-16.29,-8.71,-4.97,-19.51,47.66 | |
| 14 | +Excluding VIX,2514,4,10,52.87,26.28,18.07,-5.81,-9.16,-13.13,0.84,-2.73,,67.73 | |
| 15 | +Excluding BTC and ETH,2514,4,10,58.97,34.37,24.08,-4.41,-6.57,-13.75,,,-20.08, | |
| 16 | +Excluding ETH (BTC only),2514,4,10,53.79,35.74,25.04,-5.31,-7.56,-13.69,-1.25,,-19.75,91.71 | |
added
results/rev_table_rv_descriptives.csv
+11 −0
@@ -0,0 +1,11 @@ | ||
| 1 | +Asset,Class,Mean_RV_pct,Median_RV_pct,Max_RV_pct,Skew_level,Kurt_level,Skew_log,Kurt_log,AC1_log,AC22_log,ADF_log,ADF_p,KPSS_log,KPSS_p | |
| 2 | +ES,Equity,13.9130,11.2430,110.9898,3.7761,23.8098,0.6014,0.6182,0.8420,0.4064,-4.8490,0.0000,0.9802,0.0100 | |
| 3 | +NQ,Equity,17.9021,15.0912,112.1448,2.8516,14.7039,0.3803,0.2586,0.8309,0.4262,-5.2029,0.0000,1.4540,0.0100 | |
| 4 | +EURUSD,FX,7.0394,6.5410,32.2687,2.0332,8.8979,0.4123,0.4511,0.6794,0.3842,-4.8009,0.0001,0.2287,0.1000 | |
| 5 | +USDJPY,FX,7.7168,6.9371,35.2718,1.9371,6.9254,0.2838,0.1699,0.7405,0.3777,-5.2185,0.0000,0.9727,0.0100 | |
| 6 | +GBPUSD,FX,8.4415,7.6741,51.1580,3.3203,23.1694,0.7727,1.6603,0.7169,0.3390,-5.6056,0.0000,1.0798,0.0100 | |
| 7 | +GC,Commodity,13.5896,12.0959,90.6634,3.8431,28.0355,0.8315,1.7549,0.7194,0.4040,-4.3933,0.0003,1.7547,0.0100 | |
| 8 | +CL,Commodity,33.7518,28.8295,327.9404,5.8458,51.9113,1.3638,4.0017,0.8348,0.5016,-4.1446,0.0008,0.5510,0.0302 | |
| 9 | +BTC,Crypto,103.3814,53.2647,1408.7004,3.8967,19.2813,1.0159,0.8960,0.9077,0.6542,-3.4057,0.0108,2.5093,0.0100 | |
| 10 | +ETH,Crypto,113.2123,79.3054,1281.2472,4.3060,28.3030,0.5953,0.5097,0.8543,0.6590,-2.9769,0.0371,4.4558,0.0100 | |
| 11 | +VIX,Volatility,115.7782,101.4931,682.5030,2.0057,7.8973,0.1811,0.1417,0.5513,0.1179,-10.7995,0.0000,0.9862,0.0100 | |
added
results/rev_table_yearly.csv
+11 −0
@@ -0,0 +1,11 @@ | ||
| 1 | +Year,T,TSI,TSI_lo,TSI_hi,NET_BTC,NET_BTC_lo,NET_BTC_hi,NET_ETH,NET_ETH_lo,NET_ETH_hi,FROM_BTC,FROM_BTC_lo,FROM_BTC_hi,FROM_BTC_excl_ETH,BTC_from_ES,ES_from_BTC,NET_ES,NET_ES_lo,NET_ES_hi | |
| 2 | +2016,200,55.36,55.07,63.16,25.42,-13.90,50.99,1.41,-24.09,22.31,23.06,20.38,44.63,13.83,0.39,3.32,29.75,14.95,41.90 | |
| 3 | +2017,251,51.03,51.06,57.51,-3.89,-24.27,12.05,5.12,-16.53,16.98,36.37,33.12,52.59,8.68,0.22,0.02,13.80,4.76,25.26 | |
| 4 | +2018,251,51.70,50.69,59.19,17.97,-13.92,44.58,-12.60,-29.80,8.38,28.75,18.63,53.19,22.81,7.52,8.83,27.51,9.95,42.65 | |
| 5 | +2019,252,54.38,52.50,61.31,11.29,-13.27,22.32,-10.03,-25.10,5.25,21.72,19.41,42.38,6.76,0.45,0.23,30.63,17.46,41.97 | |
| 6 | +2020,253,61.50,57.73,67.64,-13.17,-32.79,11.02,-15.25,-31.74,1.58,45.17,35.13,60.56,34.36,2.32,0.94,40.57,12.49,66.50 | |
| 7 | +2021,252,60.55,57.56,66.39,-14.61,-30.62,0.06,-6.72,-29.51,10.51,49.71,43.18,60.99,23.54,4.46,1.29,33.11,16.31,46.70 | |
| 8 | +2022,254,61.20,59.86,67.10,-1.58,-14.72,12.91,1.02,-11.54,14.68,61.01,57.42,69.15,25.72,5.88,3.84,18.05,4.69,30.05 | |
| 9 | +2023,250,62.55,59.33,68.57,-11.53,-29.46,5.68,-7.43,-25.73,10.26,55.12,49.83,65.14,20.22,3.55,0.59,33.40,19.11,44.09 | |
| 10 | +2024,252,62.08,59.46,68.72,-7.65,-15.39,4.53,-10.32,-18.47,1.00,55.85,50.91,65.74,24.24,5.22,3.19,25.56,14.93,33.17 | |
| 11 | +2025,251,71.54,67.91,75.16,-3.16,-20.33,18.54,-20.18,-31.39,-4.50,65.90,58.79,73.36,46.16,10.04,7.71,38.82,22.77,51.20 | |
modified
scripts/01_analysis.py
+17 −1
@@ -1,6 +1,22 @@ | ||
| 1 | 1 | """ |
| 2 | 2 | Intraday Volatility Transmission Across Asset Classes |
| 3 | −Diebold-Yilmaz Connectedness Analysis | |
| 3 | +Diebold-Yilmaz Connectedness Analysis -- stage 1 (May 2026 pipeline) | |
| 4 | + | |
| 5 | +NOTE (revision of 2026-10-17, see docs/CHANGELOG-REVISION.md): | |
| 6 | + * This script is kept as the sole producer of results/daily_rv_all.csv and | |
| 7 | + results/table1_descriptive_stats.csv from the vendor's 5-minute DuckDB bars. | |
| 8 | + * Its sections 3-8 (VAR/GFEVD, rolling, regimes, sessions, Granger, network) | |
| 9 | + are SUPERSEDED by scripts/02_connectedness_revision.py and | |
| 10 | + scripts/03_intraday_sessions.py. Known defects of the original stages: | |
| 11 | + - the VAR panel forward-filled weekends/holidays (rv_panel.ffill(limit=5)), | |
| 12 | + so 1,137 of 3,651 rows contained stale values; | |
| 13 | + - realized volatility entered the VAR in levels, not logs; | |
| 14 | + - FirstRate time stamps are U.S. Eastern, not UTC (comment below is wrong), | |
| 15 | + so the session labels of the original Fig. 5 were shifted by 4-5 hours; | |
| 16 | + - the "session" Granger tests repeated the same daily test three times; | |
| 17 | + - 5-minute returns beyond 20 sample standard deviations are dropped before | |
| 18 | + computing RV (undisclosed in v1.0; disclosed in v1.1). | |
| 19 | + The code below is left unchanged for the audit trail. | |
| 4 | 20 | """ |
| 5 | 21 | |
| 6 | 22 | import os |
added
scripts/02_connectedness_revision.py
+677 −0
@@ -0,0 +1,677 @@ | ||
| 1 | +""" | |
| 2 | +WP 6 -- Revision of the connectedness analysis (editorial-board review, 2026-10-17). | |
| 3 | + | |
| 4 | +Starts from the daily realized-volatility panel produced by 01_analysis.py | |
| 5 | +(results/daily_rv_all.csv, annualized realized volatility per instrument and calendar day) | |
| 6 | +and re-estimates every VAR/GFEVD object on a correctly aligned panel: | |
| 7 | + | |
| 8 | + * trading-day panel: a day enters only if all ten instruments have an own realized | |
| 9 | + volatility (no forward filling; the original script forward-filled weekends and | |
| 10 | + holidays, so that 1,137 of its 3,651 rows were stale copies); | |
| 11 | + * log realized volatility (Andersen et al., 2003) instead of levels; | |
| 12 | + * VAR(4) -- HQ criterion -- with H = 10, as in the original paper; | |
| 13 | + * residual-bootstrap confidence intervals for TSI, TO, FROM, NET (Kilian, 1998); | |
| 14 | + * robustness grid (transformation, p, H, sample, weekend-inclusive crypto RV, subsets); | |
| 15 | + * rolling windows of 200 / 250 / 500 trading days; calendar-year sub-samples; | |
| 16 | + * regime sub-samples (pre-COVID, COVID crash, 2022 hiking cycle, spot-ETF era); | |
| 17 | + * Granger-causality tests with conventional F and HAC-robust Wald statistics; | |
| 18 | + * replication of the original (flawed) construction for the audit trail. | |
| 19 | + | |
| 20 | +Outputs: results/rev_*.csv, paper/tables/*.tex (generated, not typed), figures/fig*.png. | |
| 21 | +Run time: about 3 minutes on a laptop (bootstrap included). | |
| 22 | +""" | |
| 23 | +import os | |
| 24 | +import time | |
| 25 | +import warnings | |
| 26 | +import numpy as np | |
| 27 | +import pandas as pd | |
| 28 | +import matplotlib | |
| 29 | +matplotlib.use('Agg') | |
| 30 | +import matplotlib.pyplot as plt | |
| 31 | +import matplotlib.patches as mpatches | |
| 32 | +import networkx as nx | |
| 33 | +from statsmodels.tsa.api import VAR | |
| 34 | +from statsmodels.tsa.stattools import adfuller, kpss, acf | |
| 35 | +import statsmodels.api as sm | |
| 36 | + | |
| 37 | +warnings.filterwarnings('ignore') | |
| 38 | +T0 = time.time() | |
| 39 | + | |
| 40 | +ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__))) | |
| 41 | +RESULTS = os.path.join(ROOT, 'results') | |
| 42 | +FIGURES = os.path.join(ROOT, 'figures') | |
| 43 | +TABLES = os.path.join(ROOT, 'paper', 'tables') | |
| 44 | +PAPER_FIG = os.path.join(ROOT, 'paper', 'figures') | |
| 45 | +for d in (RESULTS, FIGURES, TABLES, PAPER_FIG): | |
| 46 | + os.makedirs(d, exist_ok=True) | |
| 47 | + | |
| 48 | +ASSETS = ['ES', 'NQ', 'EURUSD', 'USDJPY', 'GBPUSD', 'GC', 'CL', 'BTC', 'ETH', 'VIX'] | |
| 49 | +ASSET_CLASS = {'ES': 'Equity', 'NQ': 'Equity', 'EURUSD': 'FX', 'USDJPY': 'FX', 'GBPUSD': 'FX', | |
| 50 | + 'GC': 'Commodity', 'CL': 'Commodity', 'BTC': 'Crypto', 'ETH': 'Crypto', 'VIX': 'Volatility'} | |
| 51 | +CLASS_COLOR = {'Equity': '#1f77b4', 'FX': '#2ca02c', 'Commodity': '#ff7f0e', 'Crypto': '#9467bd', | |
| 52 | + 'Volatility': '#8c564b'} | |
| 53 | +P_BASE, H_BASE, W_BASE = 4, 10, 200 | |
| 54 | +B_BOOT = 500 | |
| 55 | +RNG = np.random.default_rng(20261017) | |
| 56 | +SAMPLE_START, SAMPLE_END = '2016-03-11', '2026-03-11' | |
| 57 | + | |
| 58 | +plt.rcParams.update({'font.size': 10, 'axes.titlesize': 11, 'axes.labelsize': 10, 'figure.dpi': 150, | |
| 59 | + 'savefig.dpi': 150, 'font.family': 'DejaVu Sans', | |
| 60 | + 'axes.spines.top': False, 'axes.spines.right': False}) | |
| 61 | + | |
| 62 | + | |
| 63 | +def log(msg): | |
| 64 | + print(f"[{time.time() - T0:6.1f}s] {msg}", flush=True) | |
| 65 | + | |
| 66 | + | |
| 67 | +def savefig(fig, name): | |
| 68 | + for d in (FIGURES, PAPER_FIG): | |
| 69 | + fig.savefig(os.path.join(d, name), dpi=150, bbox_inches='tight') | |
| 70 | + plt.close(fig) | |
| 71 | + | |
| 72 | + | |
| 73 | +# ─── 1. Panels ──────────────────────────────────────────────────────────────── | |
| 74 | +rv_all = pd.read_csv(os.path.join(RESULTS, 'daily_rv_all.csv'), parse_dates=['date']).set_index('date') | |
| 75 | +rv_all = rv_all[ASSETS] | |
| 76 | + | |
| 77 | +# (a) trading-day panel: all ten instruments observed (VIX trades only on CBOE days) | |
| 78 | +panel = rv_all.loc[SAMPLE_START:SAMPLE_END].dropna() | |
| 79 | +log(f"trading-day panel: {panel.index[0].date()} -> {panel.index[-1].date()}, T = {len(panel)}; " | |
| 80 | + f"weekday counts = {panel.index.dayofweek.value_counts().sort_index().to_dict()}") | |
| 81 | + | |
| 82 | +# (b) replication of the original construction (calendar days, forward fill up to 5 days, levels) | |
| 83 | +orig_panel = rv_all.ffill(limit=5).dropna(thresh=len(ASSETS) - 2).dropna() | |
| 84 | +n_weekend = int((orig_panel.index.dayofweek >= 5).sum()) | |
| 85 | +n_ffilled_rows = int((orig_panel.index.isin(rv_all.dropna().index) == False).sum()) | |
| 86 | +log(f"original construction: T = {len(orig_panel)}, weekend rows = {n_weekend}, " | |
| 87 | + f"rows with at least one forward-filled value = {n_ffilled_rows}") | |
| 88 | + | |
| 89 | +# (c) weekend-inclusive crypto RV: average daily variance over the calendar days since the | |
| 90 | +# previous trading day (so Monday carries Saturday, Sunday and Monday variance) | |
| 91 | +def weekend_inclusive(series, trading_days): | |
| 92 | + var = series.dropna() ** 2 | |
| 93 | + out = {} | |
| 94 | + prev = None | |
| 95 | + for d in trading_days: | |
| 96 | + if prev is None: | |
| 97 | + out[d] = var.get(d, np.nan) | |
| 98 | + else: | |
| 99 | + win = var.loc[prev + pd.Timedelta(days=1):d] | |
| 100 | + out[d] = win.mean() if len(win) else np.nan | |
| 101 | + prev = d | |
| 102 | + return pd.Series(out) ** 0.5 | |
| 103 | + | |
| 104 | + | |
| 105 | +panel_wk = panel.copy() | |
| 106 | +for c in ('BTC', 'ETH'): | |
| 107 | + panel_wk[c] = weekend_inclusive(rv_all[c], panel.index) | |
| 108 | +panel_wk = panel_wk.dropna() | |
| 109 | + | |
| 110 | + | |
| 111 | +# ─── 2. Descriptive statistics of daily RV ──────────────────────────────────── | |
| 112 | +rows = [] | |
| 113 | +for a in ASSETS: | |
| 114 | + s = panel[a] | |
| 115 | + ls = np.log(s) | |
| 116 | + adf_l = adfuller(ls, regression='c', autolag='AIC') | |
| 117 | + kp_l = kpss(ls, regression='c', nlags='auto') | |
| 118 | + rows.append({'Asset': a, 'Class': ASSET_CLASS[a], 'Mean_RV_pct': 100 * s.mean(), 'Median_RV_pct': 100 * s.median(), | |
| 119 | + 'Max_RV_pct': 100 * s.max(), 'Skew_level': s.skew(), 'Kurt_level': s.kurt(), | |
| 120 | + 'Skew_log': ls.skew(), 'Kurt_log': ls.kurt(), 'AC1_log': acf(ls, nlags=22)[1], | |
| 121 | + 'AC22_log': acf(ls, nlags=22)[22], 'ADF_log': adf_l[0], 'ADF_p': adf_l[1], | |
| 122 | + 'KPSS_log': kp_l[0], 'KPSS_p': kp_l[1]}) | |
| 123 | +desc = pd.DataFrame(rows).set_index('Asset') | |
| 124 | +desc.to_csv(os.path.join(RESULTS, 'rev_table_rv_descriptives.csv'), float_format='%.4f') | |
| 125 | +log("descriptives done") | |
| 126 | + | |
| 127 | + | |
| 128 | +# ─── 3. GFEVD machinery ─────────────────────────────────────────────────────── | |
| 129 | +def gfevd_from_var(coefs, sigma, H): | |
| 130 | + """Normalized generalized FEVD (Koop et al., 1996; Pesaran and Shin, 1998).""" | |
| 131 | + n = sigma.shape[0] | |
| 132 | + p = coefs.shape[0] | |
| 133 | + psi = [np.eye(n)] | |
| 134 | + for h in range(1, H): | |
| 135 | + acc = np.zeros((n, n)) | |
| 136 | + for j in range(1, min(h, p) + 1): | |
| 137 | + acc += coefs[j - 1] @ psi[h - j] | |
| 138 | + psi.append(acc) | |
| 139 | + num = np.zeros((n, n)) | |
| 140 | + den = np.zeros(n) | |
| 141 | + for h in range(H): | |
| 142 | + ps = psi[h] @ sigma | |
| 143 | + num += ps ** 2 | |
| 144 | + den += np.einsum('ij,ij->i', ps, psi[h]) | |
| 145 | + theta = num / (np.diag(sigma)[None, :] * den[:, None]) | |
| 146 | + return theta / theta.sum(axis=1, keepdims=True) | |
| 147 | + | |
| 148 | + | |
| 149 | +def connectedness(y, p=P_BASE, H=H_BASE): | |
| 150 | + """Fit VAR(p) with constant, return dict of connectedness objects (in percent).""" | |
| 151 | + res = VAR(y.values).fit(p, trend='c') | |
| 152 | + th = gfevd_from_var(res.coefs, res.sigma_u, H) * 100 | |
| 153 | + off = th.copy() | |
| 154 | + np.fill_diagonal(off, 0) | |
| 155 | + out = {'theta': th, 'FROM': off.sum(axis=1), 'TO': off.sum(axis=0), 'TSI': off.sum() / th.shape[0], | |
| 156 | + 'res': res} | |
| 157 | + out['NET'] = out['TO'] - out['FROM'] | |
| 158 | + out['NETPAIR'] = th.T - th # [i,j] = theta_ji - theta_ij : net from i to j | |
| 159 | + return out | |
| 160 | + | |
| 161 | + | |
| 162 | +def bootstrap_connectedness(y, p=P_BASE, H=H_BASE, B=B_BOOT, rng=RNG): | |
| 163 | + """Residual (i.i.d.) bootstrap of the VAR; returns arrays of TSI, TO, FROM, NET.""" | |
| 164 | + base = connectedness(y, p, H) | |
| 165 | + res = base['res'] | |
| 166 | + T, n = y.shape | |
| 167 | + u = res.resid - res.resid.mean(axis=0) | |
| 168 | + A = res.coefs | |
| 169 | + c = res.intercept | |
| 170 | + Y = y.values | |
| 171 | + tsi_b, to_b, from_b, net_b = [], [], [], [] | |
| 172 | + for b in range(B): | |
| 173 | + idx = rng.integers(0, len(u), len(u)) | |
| 174 | + ub = u[idx] | |
| 175 | + yb = np.empty_like(Y) | |
| 176 | + yb[:p] = Y[:p] | |
| 177 | + for t in range(p, T): | |
| 178 | + acc = c.copy() | |
| 179 | + for l in range(p): | |
| 180 | + acc += A[l] @ yb[t - l - 1] | |
| 181 | + yb[t] = acc + ub[t - p] | |
| 182 | + rb = VAR(yb).fit(p, trend='c') | |
| 183 | + th = gfevd_from_var(rb.coefs, rb.sigma_u, H) * 100 | |
| 184 | + off = th.copy() | |
| 185 | + np.fill_diagonal(off, 0) | |
| 186 | + fr, to = off.sum(axis=1), off.sum(axis=0) | |
| 187 | + tsi_b.append(off.sum() / n) | |
| 188 | + to_b.append(to) | |
| 189 | + from_b.append(fr) | |
| 190 | + net_b.append(to - fr) | |
| 191 | + return base, np.array(tsi_b), np.array(to_b), np.array(from_b), np.array(net_b) | |
| 192 | + | |
| 193 | + | |
| 194 | +def ci(arr, q=(5, 95)): | |
| 195 | + return np.percentile(arr, q, axis=0) | |
| 196 | + | |
| 197 | + | |
| 198 | +# ─── 4. Full-sample connectedness (log RV, trading days) with bootstrap ─────── | |
| 199 | +ylog = np.log(panel) | |
| 200 | +log("full-sample bootstrap ...") | |
| 201 | +base, tsi_b, to_b, from_b, net_b = bootstrap_connectedness(ylog) | |
| 202 | +tsi_ci, to_ci, from_ci, net_ci = ci(tsi_b), ci(to_b), ci(from_b), ci(net_b) | |
| 203 | +log(f"full-sample TSI = {base['TSI']:.2f} [{tsi_ci[0]:.2f}, {tsi_ci[1]:.2f}]") | |
| 204 | + | |
| 205 | +full_tbl = pd.DataFrame(base['theta'], index=ASSETS, columns=ASSETS) | |
| 206 | +full_tbl['FROM'] = base['FROM'] | |
| 207 | +full_tbl.loc['TO'] = list(base['TO']) + [base['TSI']] | |
| 208 | +full_tbl.loc['NET'] = list(base['NET']) + [np.nan] | |
| 209 | +full_tbl.to_csv(os.path.join(RESULTS, 'rev_table_connectedness_full.csv'), float_format='%.2f') | |
| 210 | +ci_tbl = pd.DataFrame({'TO': base['TO'], 'TO_lo': to_ci[0], 'TO_hi': to_ci[1], 'FROM': base['FROM'], | |
| 211 | + 'FROM_lo': from_ci[0], 'FROM_hi': from_ci[1], 'NET': base['NET'], 'NET_lo': net_ci[0], | |
| 212 | + 'NET_hi': net_ci[1]}, index=ASSETS) | |
| 213 | +ci_tbl.loc['TSI', ['NET', 'NET_lo', 'NET_hi']] = [base['TSI'], tsi_ci[0], tsi_ci[1]] | |
| 214 | +ci_tbl.to_csv(os.path.join(RESULTS, 'rev_table_connectedness_full_ci.csv'), float_format='%.2f') | |
| 215 | + | |
| 216 | +# original construction replicated (audit) and intermediate variants | |
| 217 | +orig = connectedness(orig_panel, P_BASE, H_BASE) | |
| 218 | +lvl_td = connectedness(panel, P_BASE, H_BASE) | |
| 219 | +audit = pd.DataFrame([ | |
| 220 | + {'Construction': 'Original: calendar days, forward-filled, RV levels', 'T': len(orig_panel), 'TSI': orig['TSI'], | |
| 221 | + 'NET_ES': orig['NET'][0], 'NET_NQ': orig['NET'][1], 'NET_VIX': orig['NET'][9], 'NET_BTC': orig['NET'][7], | |
| 222 | + 'NET_USDJPY': orig['NET'][3]}, | |
| 223 | + {'Construction': 'Trading days, RV levels', 'T': len(panel), 'TSI': lvl_td['TSI'], 'NET_ES': lvl_td['NET'][0], | |
| 224 | + 'NET_NQ': lvl_td['NET'][1], 'NET_VIX': lvl_td['NET'][9], 'NET_BTC': lvl_td['NET'][7], | |
| 225 | + 'NET_USDJPY': lvl_td['NET'][3]}, | |
| 226 | + {'Construction': 'Trading days, log RV (revised baseline)', 'T': len(panel), 'TSI': base['TSI'], | |
| 227 | + 'NET_ES': base['NET'][0], 'NET_NQ': base['NET'][1], 'NET_VIX': base['NET'][9], 'NET_BTC': base['NET'][7], | |
| 228 | + 'NET_USDJPY': base['NET'][3]}, | |
| 229 | +]) | |
| 230 | +audit.to_csv(os.path.join(RESULTS, 'rev_audit_construction.csv'), index=False, float_format='%.2f') | |
| 231 | +log("audit table done") | |
| 232 | + | |
| 233 | +# ─── 5. Robustness grid ─────────────────────────────────────────────────────── | |
| 234 | +rob_rows = [] | |
| 235 | + | |
| 236 | + | |
| 237 | +def rob(label, y, p=P_BASE, H=H_BASE): | |
| 238 | + r = connectedness(y, p, H) | |
| 239 | + d = {'Specification': label, 'T': len(y), 'p': p, 'H': H, 'TSI': r['TSI']} | |
| 240 | + for a in ['ES', 'NQ', 'USDJPY', 'GC', 'CL', 'BTC', 'ETH', 'VIX']: | |
| 241 | + if a in y.columns: | |
| 242 | + d[f'NET_{a}'] = r['NET'][list(y.columns).index(a)] | |
| 243 | + else: | |
| 244 | + d[f'NET_{a}'] = np.nan | |
| 245 | + if 'BTC' in y.columns: | |
| 246 | + d['Own_BTC'] = r['theta'][list(y.columns).index('BTC'), list(y.columns).index('BTC')] | |
| 247 | + rob_rows.append(d) | |
| 248 | + return r | |
| 249 | + | |
| 250 | + | |
| 251 | +rob('Baseline: log RV, trading days, VAR(4), H = 10', ylog) | |
| 252 | +rob('RV in levels (trading days)', panel) | |
| 253 | +for p in (1, 2, 3, 6): | |
| 254 | + rob(f'VAR({p})', ylog, p=p) | |
| 255 | +for H in (5, 20): | |
| 256 | + rob(f'H = {H}', ylog, H=H) | |
| 257 | +rob('Weekend-inclusive crypto RV', np.log(panel_wk)) | |
| 258 | +rob('Sample 2018-01 to 2026-03', ylog.loc['2018-01-01':]) | |
| 259 | +rob('Sample 2016-03 to 2019-12', ylog.loc[:'2019-12-31']) | |
| 260 | +rob('Sample 2020-01 to 2026-03', ylog.loc['2020-01-01':]) | |
| 261 | +rob('Excluding VIX', ylog.drop(columns=['VIX'])) | |
| 262 | +rob('Excluding BTC and ETH', ylog.drop(columns=['BTC', 'ETH'])) | |
| 263 | +rob('Excluding ETH (BTC only)', ylog.drop(columns=['ETH'])) | |
| 264 | +rob_df = pd.DataFrame(rob_rows) | |
| 265 | +rob_df.to_csv(os.path.join(RESULTS, 'rev_table_robustness.csv'), index=False, float_format='%.2f') | |
| 266 | +log("robustness grid done") | |
| 267 | + | |
| 268 | +# ─── 6. Rolling windows ─────────────────────────────────────────────────────── | |
| 269 | +def rolling(y, w, p=P_BASE, H=H_BASE): | |
| 270 | + dates, tsi, net = [], [], [] | |
| 271 | + Y = y.values | |
| 272 | + for i in range(len(y) - w + 1): | |
| 273 | + r = VAR(Y[i:i + w]).fit(p, trend='c') | |
| 274 | + th = gfevd_from_var(r.coefs, r.sigma_u, H) * 100 | |
| 275 | + off = th.copy() | |
| 276 | + np.fill_diagonal(off, 0) | |
| 277 | + dates.append(y.index[i + w - 1]) | |
| 278 | + tsi.append(off.sum() / th.shape[0]) | |
| 279 | + net.append(off.sum(axis=0) - off.sum(axis=1)) | |
| 280 | + out = pd.DataFrame(net, index=dates, columns=[f'NET_{a}' for a in y.columns]) | |
| 281 | + out.insert(0, 'TSI', tsi) | |
| 282 | + out.index.name = 'date' | |
| 283 | + return out | |
| 284 | + | |
| 285 | + | |
| 286 | +roll = {} | |
| 287 | +for w in (200, 250, 500): | |
| 288 | + roll[w] = rolling(ylog, w) | |
| 289 | + roll[w].to_csv(os.path.join(RESULTS, f'rev_rolling_w{w}.csv'), float_format='%.3f') | |
| 290 | + log(f"rolling w={w}: {len(roll[w])} windows, TSI mean {roll[w]['TSI'].mean():.2f}, " | |
| 291 | + f"min {roll[w]['TSI'].min():.2f} ({roll[w]['TSI'].idxmin().date()}), " | |
| 292 | + f"max {roll[w]['TSI'].max():.2f} ({roll[w]['TSI'].idxmax().date()})") | |
| 293 | +roll_orig = pd.read_csv(os.path.join(RESULTS, 'rolling_total_spillover.csv'), parse_dates=['date']).set_index('date') | |
| 294 | +roll_summary = pd.DataFrame({ | |
| 295 | + 'window': ['original (200 calendar days, levels, forward-filled)', '200 trading days', '250 trading days', | |
| 296 | + '500 trading days'], | |
| 297 | + 'n_windows': [len(roll_orig), len(roll[200]), len(roll[250]), len(roll[500])], | |
| 298 | + 'mean': [roll_orig['total_spillover'].mean()] + [roll[w]['TSI'].mean() for w in (200, 250, 500)], | |
| 299 | + 'min': [roll_orig['total_spillover'].min()] + [roll[w]['TSI'].min() for w in (200, 250, 500)], | |
| 300 | + 'min_date': [roll_orig['total_spillover'].idxmin().date()] + [roll[w]['TSI'].idxmin().date() for w in (200, 250, 500)], | |
| 301 | + 'max': [roll_orig['total_spillover'].max()] + [roll[w]['TSI'].max() for w in (200, 250, 500)], | |
| 302 | + 'max_date': [roll_orig['total_spillover'].idxmax().date()] + [roll[w]['TSI'].idxmax().date() for w in (200, 250, 500)], | |
| 303 | +}) | |
| 304 | +roll_summary.to_csv(os.path.join(RESULTS, 'rev_rolling_summary.csv'), index=False, float_format='%.2f') | |
| 305 | + | |
| 306 | +# ─── 7. Regimes (with bootstrap CIs on NET) ─────────────────────────────────── | |
| 307 | +REGIMES = { | |
| 308 | + 'Pre-COVID (2019-01 to 2020-02)': ('2019-01-01', '2020-02-28'), | |
| 309 | + 'COVID crash (2020-03 to 2020-06)': ('2020-03-01', '2020-06-30'), | |
| 310 | + 'Rate hikes (2022-01 to 2022-12)': ('2022-01-01', '2022-12-31'), | |
| 311 | + 'Spot-ETF era (2024-01 to 2026-03)': ('2024-01-11', '2026-03-11'), | |
| 312 | +} | |
| 313 | +reg_rows, reg_full = [], {} | |
| 314 | +for name, (s, e) in REGIMES.items(): | |
| 315 | + y = ylog.loc[s:e] | |
| 316 | + p = P_BASE if len(y) >= 150 else 1 | |
| 317 | + b, tb, tob, frb, nb = bootstrap_connectedness(y, p=p, B=B_BOOT) | |
| 318 | + tci, nci = ci(tb), ci(nb) | |
| 319 | + row = {'Regime': name, 'T': len(y), 'p': p, 'TSI': b['TSI'], 'TSI_lo': tci[0], 'TSI_hi': tci[1]} | |
| 320 | + for k, a in enumerate(ASSETS): | |
| 321 | + row[f'NET_{a}'] = b['NET'][k] | |
| 322 | + row[f'NET_{a}_lo'] = nci[0][k] | |
| 323 | + row[f'NET_{a}_hi'] = nci[1][k] | |
| 324 | + reg_rows.append(row) | |
| 325 | + tbl = pd.DataFrame(b['theta'], index=ASSETS, columns=ASSETS) | |
| 326 | + tbl['FROM'] = b['FROM'] | |
| 327 | + tbl.loc['TO'] = list(b['TO']) + [b['TSI']] | |
| 328 | + tbl.loc['NET'] = list(b['NET']) + [np.nan] | |
| 329 | + reg_full[name] = tbl | |
| 330 | + slug = name.split(' (')[0].lower().replace(' ', '_').replace('-', '') | |
| 331 | + tbl.to_csv(os.path.join(RESULTS, f'rev_table_regime_{slug}.csv'), float_format='%.2f') | |
| 332 | + log(f"regime {name}: T={len(y)}, p={p}, TSI={b['TSI']:.1f} [{tci[0]:.1f},{tci[1]:.1f}], " | |
| 333 | + f"NET BTC={b['NET'][7]:+.1f} [{nci[0][7]:+.1f},{nci[1][7]:+.1f}], NET USDJPY={b['NET'][3]:+.1f}") | |
| 334 | + # same regime with p = 4 for comparison when p = 1 was used | |
| 335 | + if p != P_BASE: | |
| 336 | + alt = connectedness(y, P_BASE, H_BASE) | |
| 337 | + log(f" (VAR(4) on the same window: TSI={alt['TSI']:.1f}, NET USDJPY={alt['NET'][3]:+.1f}, " | |
| 338 | + f"NET BTC={alt['NET'][7]:+.1f})") | |
| 339 | + reg_rows[-1]['TSI_var4'] = alt['TSI'] | |
| 340 | + reg_rows[-1]['NET_USDJPY_var4'] = alt['NET'][3] | |
| 341 | + reg_rows[-1]['NET_BTC_var4'] = alt['NET'][7] | |
| 342 | +reg_df = pd.DataFrame(reg_rows) | |
| 343 | +reg_df.to_csv(os.path.join(RESULTS, 'rev_table_regimes.csv'), index=False, float_format='%.2f') | |
| 344 | + | |
| 345 | +# ─── 8. Calendar-year sub-samples (crypto integration) ──────────────────────── | |
| 346 | +yr_rows = [] | |
| 347 | +for yr in range(2016, 2027): | |
| 348 | + y = ylog.loc[str(yr)] | |
| 349 | + if len(y) < 60: | |
| 350 | + continue | |
| 351 | + b, tb, tob, frb, nb = bootstrap_connectedness(y, p=1 if len(y) < 150 else 2, B=300) | |
| 352 | + tci, nci = ci(tb), ci(nb) | |
| 353 | + i_btc, i_es, i_eth = ASSETS.index('BTC'), ASSETS.index('ES'), ASSETS.index('ETH') | |
| 354 | + th = b['theta'] | |
| 355 | + yr_rows.append({'Year': yr, 'T': len(y), 'TSI': b['TSI'], 'TSI_lo': tci[0], 'TSI_hi': tci[1], | |
| 356 | + 'NET_BTC': b['NET'][i_btc], 'NET_BTC_lo': nci[0][i_btc], 'NET_BTC_hi': nci[1][i_btc], | |
| 357 | + 'NET_ETH': b['NET'][i_eth], 'NET_ETH_lo': nci[0][i_eth], 'NET_ETH_hi': nci[1][i_eth], | |
| 358 | + 'FROM_BTC': b['FROM'][i_btc], 'FROM_BTC_lo': ci(frb)[0][i_btc], 'FROM_BTC_hi': ci(frb)[1][i_btc], | |
| 359 | + 'FROM_BTC_excl_ETH': b['FROM'][i_btc] - th[i_btc, i_eth], | |
| 360 | + 'BTC_from_ES': th[i_btc, i_es], 'ES_from_BTC': th[i_es, i_btc], | |
| 361 | + 'NET_ES': b['NET'][i_es], 'NET_ES_lo': nci[0][i_es], 'NET_ES_hi': nci[1][i_es]}) | |
| 362 | +yr_df = pd.DataFrame(yr_rows) | |
| 363 | +yr_df.to_csv(os.path.join(RESULTS, 'rev_table_yearly.csv'), index=False, float_format='%.2f') | |
| 364 | +log("yearly sub-samples done") | |
| 365 | + | |
| 366 | +# ─── 9. Granger causality (log RV, p lags, F and HAC Wald) ──────────────────── | |
| 367 | +PAIRS = [('ES', 'VIX'), ('NQ', 'VIX'), ('VIX', 'ES'), ('VIX', 'NQ'), ('ES', 'NQ'), ('NQ', 'ES'), | |
| 368 | + ('ES', 'BTC'), ('NQ', 'BTC'), ('VIX', 'BTC'), ('BTC', 'ES'), ('BTC', 'NQ'), ('BTC', 'VIX'), | |
| 369 | + ('USDJPY', 'ES'), ('ES', 'USDJPY'), ('GC', 'BTC'), ('BTC', 'GC')] | |
| 370 | + | |
| 371 | + | |
| 372 | +def granger(y, cause, effect, p=P_BASE, hac_lags=10): | |
| 373 | + df = pd.DataFrame({'y': y[effect], 'x': y[cause]}) | |
| 374 | + X = pd.concat([df['y'].shift(l).rename(f'y_l{l}') for l in range(1, p + 1)] + | |
| 375 | + [df['x'].shift(l).rename(f'x_l{l}') for l in range(1, p + 1)], axis=1) | |
| 376 | + X = sm.add_constant(X) | |
| 377 | + data = pd.concat([df['y'], X], axis=1).dropna() | |
| 378 | + yy, XX = data['y'], data.drop(columns='y') | |
| 379 | + m_u = sm.OLS(yy, XX).fit() | |
| 380 | + m_r = sm.OLS(yy, XX[[c for c in XX.columns if not c.startswith('x_')]]).fit() | |
| 381 | + T = len(yy) | |
| 382 | + F = ((m_r.ssr - m_u.ssr) / p) / (m_u.ssr / (T - 2 * p - 1)) | |
| 383 | + from scipy import stats | |
| 384 | + pF = 1 - stats.f.cdf(F, p, T - 2 * p - 1) | |
| 385 | + m_hac = sm.OLS(yy, XX).fit(cov_type='HAC', cov_kwds={'maxlags': hac_lags}) | |
| 386 | + R = np.zeros((p, XX.shape[1])) | |
| 387 | + for k, c in enumerate([c for c in XX.columns if c.startswith('x_')]): | |
| 388 | + R[k, list(XX.columns).index(c)] = 1 | |
| 389 | + w = m_hac.wald_test(R, use_f=False, scalar=True) | |
| 390 | + return {'Cause': cause, 'Effect': effect, 'T': T, 'F': F, 'p_F': pF, 'Wald_HAC': float(w.statistic), | |
| 391 | + 'p_HAC': float(w.pvalue), 'sum_coef': float(m_u.params[[c for c in XX.columns if c.startswith('x_')]].sum())} | |
| 392 | + | |
| 393 | + | |
| 394 | +gr = pd.DataFrame([granger(ylog, c, e) for c, e in PAIRS]) | |
| 395 | +gr.to_csv(os.path.join(RESULTS, 'rev_table_granger.csv'), index=False, float_format='%.4f') | |
| 396 | +log("Granger tests done") | |
| 397 | + | |
| 398 | +# ─── 10. Lag-order criteria ─────────────────────────────────────────────────── | |
| 399 | +sel = VAR(ylog.values).select_order(maxlags=10) | |
| 400 | +lag_tbl = pd.DataFrame({'p': range(0, 11), 'AIC': sel.ics['aic'], 'BIC': sel.ics['bic'], 'HQ': sel.ics['hqic']}) | |
| 401 | +lag_tbl.to_csv(os.path.join(RESULTS, 'rev_table_lag_selection.csv'), index=False, float_format='%.3f') | |
| 402 | +log(f"lag selection: {sel.selected_orders}") | |
| 403 | + | |
| 404 | + | |
| 405 | +# ─── 11. LaTeX tables (generated) ───────────────────────────────────────────── | |
| 406 | +def fmt(x, d=1, sign=False): | |
| 407 | + if pd.isna(x): | |
| 408 | + return '' | |
| 409 | + s = f"{x:+.{d}f}" if sign else f"{x:.{d}f}" | |
| 410 | + return s.replace('-', '$-$').replace('+', '$+$') if sign else s | |
| 411 | + | |
| 412 | + | |
| 413 | +def write(name, text): | |
| 414 | + with open(os.path.join(TABLES, name), 'w') as f: | |
| 415 | + f.write(text) | |
| 416 | + | |
| 417 | + | |
| 418 | +# 11a. RV descriptives | |
| 419 | +lines = [r"\begin{tabular}{@{}llrrrrrrrrr@{}}", r"\toprule", | |
| 420 | + r"Asset & Class & Mean & Median & Max & Skew & Skew & Kurt & $\rho_1$ & ADF & KPSS \\", | |
| 421 | + r" & & \multicolumn{3}{c}{annualized RV (\%)} & level & log & log & log & log & log \\", | |
| 422 | + r"\cmidrule(lr){3-5}\cmidrule(lr){6-6}\cmidrule(lr){7-9}\cmidrule(lr){10-11}"] | |
| 423 | +lines[-1] = r"\midrule" | |
| 424 | +for a in ASSETS: | |
| 425 | + r = desc.loc[a] | |
| 426 | + kp = fmt(r['KPSS_log'], 2) + ('' if r['KPSS_p'] > 0.05 else r'$^{*}$') | |
| 427 | + adf_st = r'$^{***}$' if r['ADF_p'] < 0.01 else r'$^{**}$' if r['ADF_p'] < 0.05 else r'$^{*}$' if r['ADF_p'] < 0.10 else '' | |
| 428 | + lines.append(f"{a} & {r['Class']} & {fmt(r['Mean_RV_pct'])} & {fmt(r['Median_RV_pct'])} & {fmt(r['Max_RV_pct'], 0)} & " | |
| 429 | + f"{fmt(r['Skew_level'], 2)} & {fmt(r['Skew_log'], 2)} & {fmt(r['Kurt_log'], 2)} & {fmt(r['AC1_log'], 2)} & " | |
| 430 | + f"{fmt(r['ADF_log'], 1)}{adf_st} & {kp} \\\\") | |
| 431 | +lines += [r"\bottomrule", r"\end{tabular}"] | |
| 432 | +write('tab_rv_descriptives.tex', "\n".join(lines)) | |
| 433 | + | |
| 434 | +# 11b. full connectedness table (with CI rows) | |
| 435 | +def conn_table_tex(tbl, to_ci_=None, from_ci_=None, net_ci_=None, tsi_ci_=None): | |
| 436 | + cols = ASSETS | |
| 437 | + L = [r"\begin{tabular}{@{}l*{10}{r}r@{}}", r"\toprule", | |
| 438 | + r"& \multicolumn{10}{c}{Shock origin $j$} & \\", r"\cmidrule(lr){2-11}", | |
| 439 | + "Recipient $i$ & " + " & ".join(cols) + r" & FROM \\", r"\midrule"] | |
| 440 | + for i, a in enumerate(cols): | |
| 441 | + vals = [fmt(tbl.loc[a, c], 1) for c in cols] | |
| 442 | + vals = [f"\\textbf{{{v}}}" if c == a else v for v, c in zip(vals, cols)] | |
| 443 | + L.append(f"{a} & " + " & ".join(vals) + f" & {fmt(tbl.loc[a, 'FROM'], 1)} \\\\") | |
| 444 | + if from_ci_ is not None: | |
| 445 | + L.append(" & " + " & ".join([''] * 10) + f" & {{\\scriptsize[{fmt(from_ci_[0][i], 1)}, {fmt(from_ci_[1][i], 1)}]}} \\\\") | |
| 446 | + L.append(r"\midrule") | |
| 447 | + L.append("TO & " + " & ".join(fmt(tbl.loc['TO', c], 1) for c in cols) + f" & \\textbf{{{fmt(tbl.loc['TO', 'FROM'], 1)}}} \\\\") | |
| 448 | + if to_ci_ is not None: | |
| 449 | + L.append(" & " + " & ".join(f"{{\\scriptsize[{fmt(to_ci_[0][k], 1)}, {fmt(to_ci_[1][k], 1)}]}}" for k in range(10)) + | |
| 450 | + f" & {{\\scriptsize[{fmt(tsi_ci_[0], 1)}, {fmt(tsi_ci_[1], 1)}]}} \\\\") | |
| 451 | + L.append("NET & " + " & ".join(fmt(tbl.loc['NET', c], 1, sign=True) for c in cols) + r" & \\") | |
| 452 | + if net_ci_ is not None: | |
| 453 | + L.append(" & " + " & ".join(f"{{\\scriptsize[{fmt(net_ci_[0][k], 1, True)}, {fmt(net_ci_[1][k], 1, True)}]}}" for k in range(10)) + r" & \\") | |
| 454 | + L += [r"\bottomrule", r"\end{tabular}"] | |
| 455 | + return "\n".join(L) | |
| 456 | + | |
| 457 | + | |
| 458 | +write('tab_connectedness_full.tex', conn_table_tex(full_tbl, to_ci, from_ci, net_ci, tsi_ci)) | |
| 459 | +for name, tbl in reg_full.items(): | |
| 460 | + slug = name.split(' (')[0].lower().replace(' ', '_').replace('-', '') | |
| 461 | + write(f'tab_regime_{slug}.tex', conn_table_tex(tbl)) | |
| 462 | + | |
| 463 | +# 11c. audit / construction table | |
| 464 | +L = [r"\begin{tabular}{@{}lrrrrrrr@{}}", r"\toprule", | |
| 465 | + r"Construction of the panel & $T$ & TSI & ES & NQ & VIX & BTC & USDJPY \\", r"\midrule"] | |
| 466 | +for _, r in audit.iterrows(): | |
| 467 | + L.append(f"{r['Construction']} & {int(r['T'])} & {fmt(r['TSI'])} & {fmt(r['NET_ES'], 1, True)} & {fmt(r['NET_NQ'], 1, True)} & " | |
| 468 | + f"{fmt(r['NET_VIX'], 1, True)} & {fmt(r['NET_BTC'], 1, True)} & {fmt(r['NET_USDJPY'], 1, True)} \\\\") | |
| 469 | +L += [r"\bottomrule", r"\end{tabular}"] | |
| 470 | +write('tab_audit_construction.tex', "\n".join(L)) | |
| 471 | + | |
| 472 | +# 11d. robustness grid | |
| 473 | +L = [r"\begin{tabular}{@{}lrrrrrrrrr@{}}", r"\toprule", | |
| 474 | + r"Specification & $T$ & TSI & ES & NQ & USDJPY & CL & BTC & VIX & BTC own \\", r"\midrule"] | |
| 475 | +for _, r in rob_df.iterrows(): | |
| 476 | + L.append(f"{r['Specification']} & {int(r['T'])} & {fmt(r['TSI'])} & {fmt(r['NET_ES'], 1, True)} & {fmt(r['NET_NQ'], 1, True)} & " | |
| 477 | + f"{fmt(r['NET_USDJPY'], 1, True)} & {fmt(r['NET_CL'], 1, True)} & {fmt(r['NET_BTC'], 1, True)} & " | |
| 478 | + f"{fmt(r['NET_VIX'], 1, True)} & {fmt(r.get('Own_BTC', np.nan))} \\\\") | |
| 479 | +L += [r"\bottomrule", r"\end{tabular}"] | |
| 480 | +write('tab_robustness.tex', "\n".join(L)) | |
| 481 | + | |
| 482 | +# 11e. regimes summary with CIs | |
| 483 | +L = [r"\begin{tabular}{@{}l" + "r" * len(REGIMES) + "@{}}", r"\toprule", | |
| 484 | + " & " + " & ".join(n.split(' (')[0] for n in REGIMES) + r" \\", | |
| 485 | + " & " + " & ".join("{\\scriptsize " + n.split(' (')[1].rstrip(')') + "}" for n in REGIMES) + r" \\", r"\midrule", | |
| 486 | + "$T$ (trading days) & " + " & ".join(str(int(r['T'])) for _, r in reg_df.iterrows()) + r" \\", | |
| 487 | + "VAR lag $p$ & " + " & ".join(str(int(r['p'])) for _, r in reg_df.iterrows()) + r" \\", | |
| 488 | + "TSI (\\%) & " + " & ".join(fmt(r['TSI']) for _, r in reg_df.iterrows()) + r" \\", | |
| 489 | + " & " + " & ".join(f"{{\\scriptsize[{fmt(r['TSI_lo'])}, {fmt(r['TSI_hi'])}]}}" for _, r in reg_df.iterrows()) + r" \\", | |
| 490 | + r"\midrule", r"\multicolumn{" + str(1 + len(REGIMES)) + r"}{@{}l}{\textit{Net directional spillovers (pp)}} \\"] | |
| 491 | +for a in ASSETS: | |
| 492 | + L.append(f"{a} & " + " & ".join(fmt(r[f'NET_{a}'], 1, True) for _, r in reg_df.iterrows()) + r" \\") | |
| 493 | + L.append(" & " + " & ".join(f"{{\\scriptsize[{fmt(r[f'NET_{a}_lo'], 1, True)}, {fmt(r[f'NET_{a}_hi'], 1, True)}]}}" | |
| 494 | + for _, r in reg_df.iterrows()) + r" \\") | |
| 495 | +L += [r"\bottomrule", r"\end{tabular}"] | |
| 496 | +write('tab_regimes.tex', "\n".join(L)) | |
| 497 | + | |
| 498 | +# 11f. yearly table | |
| 499 | +L = [r"\begin{tabular}{@{}lrrrrrrr@{}}", r"\toprule", | |
| 500 | + r"Year & $T$ & TSI & NET BTC & NET ETH & FROM BTC & BTC $\leftarrow$ ES & ES $\leftarrow$ BTC \\", | |
| 501 | + r" & & (\%) & (pp) & (pp) & excl.\ ETH (\%) & (\%) & (\%) \\", r"\midrule"] | |
| 502 | +for _, r in yr_df.iterrows(): | |
| 503 | + L.append(f"{int(r['Year'])} & {int(r['T'])} & {fmt(r['TSI'])} {{\\scriptsize[{fmt(r['TSI_lo'])}, {fmt(r['TSI_hi'])}]}} & " | |
| 504 | + f"{fmt(r['NET_BTC'], 1, True)} {{\\scriptsize[{fmt(r['NET_BTC_lo'], 1, True)}, {fmt(r['NET_BTC_hi'], 1, True)}]}} & " | |
| 505 | + f"{fmt(r['NET_ETH'], 1, True)} & {fmt(r['FROM_BTC_excl_ETH'])} & {fmt(r['BTC_from_ES'])} & {fmt(r['ES_from_BTC'])} \\\\") | |
| 506 | +L += [r"\bottomrule", r"\end{tabular}"] | |
| 507 | +write('tab_yearly.tex', "\n".join(L)) | |
| 508 | + | |
| 509 | +# 11g. Granger | |
| 510 | +def stars(p): | |
| 511 | + return r'$^{***}$' if p < 0.01 else r'$^{**}$' if p < 0.05 else r'$^{*}$' if p < 0.10 else '' | |
| 512 | + | |
| 513 | + | |
| 514 | +L = [r"\begin{tabular}{@{}llrrrrr@{}}", r"\toprule", | |
| 515 | + r"Cause & Effect & $T$ & $F$ & $p$ & Wald (HAC) & $p$ \\", r"\midrule"] | |
| 516 | +for _, r in gr.iterrows(): | |
| 517 | + L.append(f"{r['Cause']} & {r['Effect']} & {int(r['T'])} & {fmt(r['F'], 2)}{stars(r['p_F'])} & {fmt(r['p_F'], 3)} & " | |
| 518 | + f"{fmt(r['Wald_HAC'], 2)}{stars(r['p_HAC'])} & {fmt(r['p_HAC'], 3)} \\\\") | |
| 519 | +L += [r"\bottomrule", r"\end{tabular}"] | |
| 520 | +write('tab_granger.tex', "\n".join(L)) | |
| 521 | + | |
| 522 | +# 11h. lag selection | |
| 523 | +L = [r"\begin{tabular}{@{}lrrrrrrrrrr@{}}", r"\toprule", "Criterion & " + " & ".join(f"$p={p}$" for p in range(1, 11)) + r" \\", r"\midrule"] | |
| 524 | +for crit in ('AIC', 'BIC', 'HQ'): | |
| 525 | + vals = lag_tbl[crit].values[1:] | |
| 526 | + best = np.argmin(vals) | |
| 527 | + L.append(f"{crit} & " + " & ".join((f"\\textbf{{{v:.2f}}}" if k == best else f"{v:.2f}") for k, v in enumerate(vals)) + r" \\") | |
| 528 | +L += [r"\bottomrule", r"\end{tabular}"] | |
| 529 | +write('tab_lag_selection.tex', "\n".join(L)) | |
| 530 | + | |
| 531 | +# 11i. rolling summary | |
| 532 | +L = [r"\begin{tabular}{@{}lrrrrrr@{}}", r"\toprule", r"Window & Windows & Mean & Min & (date) & Max & (date) \\", r"\midrule"] | |
| 533 | +for _, r in roll_summary.iterrows(): | |
| 534 | + L.append(f"{r['window']} & {int(r['n_windows'])} & {fmt(r['mean'])} & {fmt(r['min'])} & {r['min_date']} & {fmt(r['max'])} & {r['max_date']} \\\\") | |
| 535 | +L += [r"\bottomrule", r"\end{tabular}"] | |
| 536 | +write('tab_rolling_summary.tex', "\n".join(L)) | |
| 537 | +log("LaTeX tables written") | |
| 538 | + | |
| 539 | +# ─── 12. Figures ────────────────────────────────────────────────────────────── | |
| 540 | +# Fig 2: heatmap | |
| 541 | +fig, ax = plt.subplots(figsize=(10, 7.5)) | |
| 542 | +mat = base['theta'] | |
| 543 | +im = ax.imshow(mat, cmap='Blues', vmin=0, vmax=mat.max()) | |
| 544 | +for i in range(10): | |
| 545 | + for j in range(10): | |
| 546 | + ax.text(j, i, f"{mat[i, j]:.1f}", ha='center', va='center', fontsize=8, | |
| 547 | + color='white' if mat[i, j] > 0.55 * mat.max() else 'black') | |
| 548 | +ax.set_xticks(range(10)); ax.set_yticks(range(10)) | |
| 549 | +ax.set_xticklabels(ASSETS, rotation=45, ha='right'); ax.set_yticklabels(ASSETS) | |
| 550 | +ax.set_xlabel('Shock origin $j$'); ax.set_ylabel('Recipient $i$') | |
| 551 | +ax.set_title(f'Generalized FEVD shares (%), log RV, VAR(4), H = 10 — TSI = {base["TSI"]:.1f}%') | |
| 552 | +plt.colorbar(im, ax=ax, label='% of 10-day forecast-error variance') | |
| 553 | +plt.tight_layout(); savefig(fig, 'fig2_connectedness_heatmap.png') | |
| 554 | + | |
| 555 | +# Fig 3: rolling TSI (three windows) + original for reference | |
| 556 | +fig, ax = plt.subplots(figsize=(13, 5)) | |
| 557 | +ax.plot(roll[200].index, roll[200]['TSI'], color='#1f77b4', lw=1.0, label='200 trading days') | |
| 558 | +ax.plot(roll[250].index, roll[250]['TSI'], color='#ff7f0e', lw=0.9, alpha=0.9, label='250 trading days') | |
| 559 | +ax.plot(roll[500].index, roll[500]['TSI'], color='#2ca02c', lw=1.3, label='500 trading days') | |
| 560 | +ax.axhline(base['TSI'], color='gray', ls='--', lw=0.8, label=f'full sample ({base["TSI"]:.1f}%)') | |
| 561 | +events = {'COVID crash\n(Mar 2020)': '2020-03-16', 'First Fed hike\n(Mar 2022)': '2022-03-16', | |
| 562 | + 'FTX\n(Nov 2022)': '2022-11-11', 'Spot BTC ETFs\n(Jan 2024)': '2024-01-11', 'Volatility spike\n(Aug 2024)': '2024-08-05'} | |
| 563 | +for k, (lab, d) in enumerate(events.items()): | |
| 564 | + d = pd.Timestamp(d) | |
| 565 | + ax.axvline(d, color='k', ls=':', lw=0.8, alpha=0.6) | |
| 566 | + ax.text(d, ax.get_ylim()[1] - (k % 2) * 3, lab, ha='center', va='top', fontsize=7) | |
| 567 | +ax.set_ylabel('Total spillover index (%)'); ax.set_xlabel('End of window') | |
| 568 | +ax.set_title('Rolling total spillover index — log RV, VAR(4), H = 10, trading-day panel') | |
| 569 | +ax.legend(loc='lower left', ncol=4, fontsize=8) | |
| 570 | +plt.tight_layout(); savefig(fig, 'fig3_rolling_spillover.png') | |
| 571 | + | |
| 572 | +# Fig 4: NET by regime with CI bars | |
| 573 | +fig, ax = plt.subplots(figsize=(12, 5.5)) | |
| 574 | +x = np.arange(10); nreg = len(REGIMES); width = 0.8 / nreg | |
| 575 | +pal = ['#1f77b4', '#d62728', '#ff7f0e', '#9467bd'] | |
| 576 | +for k, (_, r) in enumerate(reg_df.iterrows()): | |
| 577 | + vals = np.array([r[f'NET_{a}'] for a in ASSETS]) | |
| 578 | + lo = np.array([r[f'NET_{a}_lo'] for a in ASSETS]); hi = np.array([r[f'NET_{a}_hi'] for a in ASSETS]) | |
| 579 | + off = (k - (nreg - 1) / 2) * width | |
| 580 | + ax.bar(x + off, vals, width * 0.9, color=pal[k], alpha=0.85, label=f"{r['Regime']} (TSI {r['TSI']:.1f}%)") | |
| 581 | + ax.errorbar(x + off, vals, yerr=[vals - lo, hi - vals], fmt='none', ecolor='k', elinewidth=0.6, capsize=1.5) | |
| 582 | +ax.axhline(0, color='k', lw=0.8); ax.set_xticks(x); ax.set_xticklabels(ASSETS) | |
| 583 | +ax.set_ylabel('Net directional spillover (pp)'); ax.legend(fontsize=8) | |
| 584 | +ax.set_title('Net directional spillovers by regime, with 90% bootstrap intervals') | |
| 585 | +plt.tight_layout(); savefig(fig, 'fig4_net_spillovers_regimes.png') | |
| 586 | + | |
| 587 | +# Fig 6: rolling NET BTC vs ES (w = 200 and 500) | |
| 588 | +fig, ax = plt.subplots(figsize=(13, 5)) | |
| 589 | +ax.plot(roll[200].index, roll[200]['NET_BTC'], color='#9467bd', lw=0.8, alpha=0.6, label='BTC, 200 days') | |
| 590 | +ax.plot(roll[500].index, roll[500]['NET_BTC'], color='#9467bd', lw=1.6, label='BTC, 500 days') | |
| 591 | +ax.plot(roll[200].index, roll[200]['NET_ES'], color='#1f77b4', lw=0.8, alpha=0.6, label='ES, 200 days') | |
| 592 | +ax.plot(roll[500].index, roll[500]['NET_ES'], color='#1f77b4', lw=1.6, label='ES, 500 days') | |
| 593 | +ax.axhline(0, color='k', lw=0.8, ls='--') | |
| 594 | +for lab, d in events.items(): | |
| 595 | + ax.axvline(pd.Timestamp(d), color='k', ls=':', lw=0.8, alpha=0.6) | |
| 596 | +ax.set_ylabel('Net directional spillover (pp)'); ax.set_xlabel('End of window') | |
| 597 | +ax.set_title('Rolling net directional spillovers: Bitcoin and E-mini S&P 500') | |
| 598 | +ax.legend(ncol=4, fontsize=8, loc='lower left') | |
| 599 | +plt.tight_layout(); savefig(fig, 'fig6_net_directional_btc_es.png') | |
| 600 | + | |
| 601 | +# Fig 7: network of net pairwise directional spillovers | |
| 602 | +netpair = base['NETPAIR'] | |
| 603 | +thr = np.percentile(np.abs(netpair[np.triu_indices(10, 1)]), 60) | |
| 604 | +G = nx.DiGraph() | |
| 605 | +for a in ASSETS: | |
| 606 | + G.add_node(a) | |
| 607 | +for i, a in enumerate(ASSETS): | |
| 608 | + for j, b in enumerate(ASSETS): | |
| 609 | + if i < j: | |
| 610 | + v = netpair[i, j] | |
| 611 | + if abs(v) > thr: | |
| 612 | + if v > 0: | |
| 613 | + G.add_edge(a, b, weight=v) | |
| 614 | + else: | |
| 615 | + G.add_edge(b, a, weight=-v) | |
| 616 | +order = ['ES', 'NQ', 'VIX', 'GC', 'CL', 'EURUSD', 'USDJPY', 'GBPUSD', 'BTC', 'ETH'] | |
| 617 | +pos = {a: (np.cos(2 * np.pi * k / 10 + np.pi / 2), np.sin(2 * np.pi * k / 10 + np.pi / 2)) for k, a in enumerate(order)} | |
| 618 | +fig, ax = plt.subplots(figsize=(10.5, 8)) | |
| 619 | +sizes = [300 + 25 * base['TO'][ASSETS.index(a)] for a in G.nodes()] | |
| 620 | +colors = [CLASS_COLOR[ASSET_CLASS[a]] for a in G.nodes()] | |
| 621 | +wts = np.array([G[u][v]['weight'] for u, v in G.edges()]) | |
| 622 | +nx.draw_networkx_edges(G, pos, ax=ax, width=0.6 + 3.5 * wts / wts.max(), alpha=0.7, edge_color='#555555', | |
| 623 | + arrows=True, arrowsize=14, connectionstyle='arc3,rad=0.12', node_size=sizes) | |
| 624 | +nx.draw_networkx_nodes(G, pos, ax=ax, node_size=sizes, node_color=colors, alpha=0.92, edgecolors='white', linewidths=1.5) | |
| 625 | +nx.draw_networkx_labels(G, pos, ax=ax, font_size=9, font_weight='bold') | |
| 626 | +ax.legend(handles=[mpatches.Patch(color=c, label=k) for k, c in CLASS_COLOR.items()], loc='upper left', fontsize=8) | |
| 627 | +ax.set_title(f'Net pairwise directional spillovers above the 60th percentile (|net| > {thr:.1f} pp)\n' | |
| 628 | + 'arrow from net transmitter to net receiver; node size proportional to TO spillover') | |
| 629 | +ax.axis('off'); plt.tight_layout(); savefig(fig, 'fig7_network_graph.png') | |
| 630 | + | |
| 631 | +# Fig 8: yearly BTC net and FROM with CIs | |
| 632 | +fig, axes = plt.subplots(1, 2, figsize=(12, 4.2)) | |
| 633 | +ax = axes[0] | |
| 634 | +ax.errorbar(yr_df['Year'], yr_df['NET_BTC'], yerr=[yr_df['NET_BTC'] - yr_df['NET_BTC_lo'], yr_df['NET_BTC_hi'] - yr_df['NET_BTC']], | |
| 635 | + fmt='o-', color='#9467bd', capsize=3, label='BTC') | |
| 636 | +ax.errorbar(yr_df['Year'], yr_df['NET_ES'], yerr=[yr_df['NET_ES'] - yr_df['NET_ES_lo'], yr_df['NET_ES_hi'] - yr_df['NET_ES']], | |
| 637 | + fmt='s-', color='#1f77b4', capsize=3, label='ES') | |
| 638 | +ax.axhline(0, color='k', lw=0.8, ls='--'); ax.set_ylabel('Net directional spillover (pp)'); ax.set_title('(a) Net spillovers by calendar year') | |
| 639 | +ax.legend() | |
| 640 | +ax = axes[1] | |
| 641 | +ax.plot(yr_df['Year'], yr_df['FROM_BTC_excl_ETH'], 'o-', color='#9467bd', label='BTC: FROM traditional assets (excl. ETH)') | |
| 642 | +ax.plot(yr_df['Year'], yr_df['BTC_from_ES'], 's--', color='#1f77b4', label='BTC $\\leftarrow$ ES') | |
| 643 | +ax.plot(yr_df['Year'], yr_df['ES_from_BTC'], '^--', color='#ff7f0e', label='ES $\\leftarrow$ BTC') | |
| 644 | +ax.set_ylabel('% of forecast-error variance'); ax.set_title('(b) Bitcoin–traditional-asset shares by year'); ax.legend(fontsize=8) | |
| 645 | +plt.tight_layout(); savefig(fig, 'fig8_yearly_crypto_integration.png') | |
| 646 | +log("figures written") | |
| 647 | + | |
| 648 | +# ─── 13. Key numbers for the paper ──────────────────────────────────────────── | |
| 649 | +key = { | |
| 650 | + 'T_panel': len(panel), 'T_original_panel': len(orig_panel), 'weekend_rows_original': n_weekend, | |
| 651 | + 'ffilled_rows_original': n_ffilled_rows, 'TSI': base['TSI'], 'TSI_lo': tsi_ci[0], 'TSI_hi': tsi_ci[1], | |
| 652 | + 'TSI_original_replicated': orig['TSI'], 'TSI_levels_trading_days': lvl_td['TSI'], | |
| 653 | +} | |
| 654 | +for k, a in enumerate(ASSETS): | |
| 655 | + key[f'NET_{a}'] = base['NET'][k]; key[f'NET_{a}_lo'] = net_ci[0][k]; key[f'NET_{a}_hi'] = net_ci[1][k] | |
| 656 | + key[f'TO_{a}'] = base['TO'][k]; key[f'FROM_{a}'] = base['FROM'][k]; key[f'OWN_{a}'] = base['theta'][k, k] | |
| 657 | +key['BTC_ETH'] = base['theta'][7, 8]; key['ETH_BTC'] = base['theta'][8, 7] | |
| 658 | +key['VIX_from_ES'] = base['theta'][9, 0]; key['VIX_from_NQ'] = base['theta'][9, 1] | |
| 659 | +key['BTC_from_traditional'] = base['FROM'][7] - base['theta'][7, 8] | |
| 660 | +key['ETH_from_traditional'] = base['FROM'][8] - base['theta'][8, 7] | |
| 661 | +for w in (200, 250, 500): | |
| 662 | + key[f'roll{w}_mean'] = roll[w]['TSI'].mean(); key[f'roll{w}_min'] = roll[w]['TSI'].min(); key[f'roll{w}_max'] = roll[w]['TSI'].max() | |
| 663 | + key[f'roll{w}_min_date'] = str(roll[w]['TSI'].idxmin().date()); key[f'roll{w}_max_date'] = str(roll[w]['TSI'].idxmax().date()) | |
| 664 | + key[f'roll{w}_last_NET_BTC'] = roll[w]['NET_BTC'].iloc[-1]; key[f'roll{w}_last_NET_ES'] = roll[w]['NET_ES'].iloc[-1] | |
| 665 | + key[f'roll{w}_NET_BTC_2025_mean'] = roll[w].loc['2025-01-01':'2025-12-31', 'NET_BTC'].mean() | |
| 666 | + r17 = roll[w].loc['2017-01-01':'2017-12-31', 'NET_BTC'] | |
| 667 | + key[f'roll{w}_NET_BTC_2017_mean'] = r17.mean() if len(r17) else np.nan | |
| 668 | + key[f'roll{w}_share_BTC_positive'] = (roll[w]['NET_BTC'] > 0).mean() | |
| 669 | +# rolling TSI around Feb 2018 and Mar 2020 | |
| 670 | +key['roll200_2018-02-02'] = roll[200]['TSI'].get(pd.Timestamp('2018-02-02'), np.nan) | |
| 671 | +key['roll200_2018-02-06'] = roll[200]['TSI'].get(pd.Timestamp('2018-02-06'), np.nan) | |
| 672 | +key['roll200_2020-02-20'] = roll[200]['TSI'].get(pd.Timestamp('2020-02-20'), np.nan) | |
| 673 | +key['roll200_2020-03-31'] = roll[200]['TSI'].get(pd.Timestamp('2020-03-31'), np.nan) | |
| 674 | +key['roll200_2020-06-30'] = roll[200]['TSI'].get(pd.Timestamp('2020-06-30'), np.nan) | |
| 675 | +pd.Series(key).to_csv(os.path.join(RESULTS, 'rev_key_numbers.csv'), header=['value']) | |
| 676 | +log("key numbers saved; done") | |
| 677 | +print(pd.Series(key).to_string()) | |
added
scripts/03_intraday_sessions.py
+276 −0
@@ -0,0 +1,276 @@ | ||
| 1 | +""" | |
| 2 | +WP 6 -- Intraday periodicity and trading-session analysis (revision, 2026-10-17). | |
| 3 | + | |
| 4 | +The original 01_analysis.py labelled FirstRate time stamps as UTC, whereas they are in | |
| 5 | +U.S. Eastern time (the ES series has its daily Globex maintenance break at 17:00 and the | |
| 6 | +VIX series starts at 03:15 / 09:30 Eastern). This script rebuilds the intraday analysis | |
| 7 | +with an explicit America/New_York -> UTC conversion from one-minute FirstRate bars held | |
| 8 | +locally (sibling repository WP 12, same vendor; path in WP6_MINUTE_DIR), aggregated to the | |
| 9 | +paper's 5-minute grid over the common sample 2016-03-11 to 2026-03-11: | |
| 10 | + | |
| 11 | + * hourly profile of average absolute 5-minute returns, in UTC, for ES, NQ, VIX, BTC; | |
| 12 | + * session realized variances (Asian 00:00-08:00, European 08:00-14:30, | |
| 13 | + U.S. 14:30-21:00 UTC) and their shares of the daily total; | |
| 14 | + * session-ordered predictive regressions: does Bitcoin's Asian/European-session | |
| 15 | + volatility help predict the U.S.-session volatility of ES (and vice versa), and | |
| 16 | + does weekend Bitcoin volatility predict Monday equity volatility? | |
| 17 | + | |
| 18 | +Outputs: results/rev_intraday_*.csv, paper/tables/tab_sessions*.tex, figures/fig5_hourly_volatility.png. | |
| 19 | +Run time: about 2 minutes (loading 1-minute parquet files). | |
| 20 | +""" | |
| 21 | +import os | |
| 22 | +import time | |
| 23 | +import warnings | |
| 24 | +import numpy as np | |
| 25 | +import pandas as pd | |
| 26 | +import matplotlib | |
| 27 | +matplotlib.use('Agg') | |
| 28 | +import matplotlib.pyplot as plt | |
| 29 | +import statsmodels.api as sm | |
| 30 | + | |
| 31 | +warnings.filterwarnings('ignore') | |
| 32 | +T0 = time.time() | |
| 33 | +ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__))) | |
| 34 | +RESULTS = os.path.join(ROOT, 'results') | |
| 35 | +FIGURES = os.path.join(ROOT, 'figures') | |
| 36 | +TABLES = os.path.join(ROOT, 'paper', 'tables') | |
| 37 | +PAPER_FIG = os.path.join(ROOT, 'paper', 'figures') | |
| 38 | +MINUTE_DIR = os.environ.get('WP6_MINUTE_DIR', os.path.join(ROOT, '..', 'realized-volatility-horse-race', 'data', 'raw')) | |
| 39 | +FILES = {'ES': 'futures_ES_1min.parquet', 'NQ': 'futures_NQ_1min.parquet', 'VIX': 'index_VIX_1min.parquet', | |
| 40 | + 'BTC': 'crypto_BTC_1min.parquet'} | |
| 41 | +START, END = '2016-03-11', '2026-03-11' | |
| 42 | +COLORS = {'ES': '#1f77b4', 'NQ': '#aec7e8', 'VIX': '#8c564b', 'BTC': '#9467bd'} | |
| 43 | +SESSIONS = {'Asian': (0.0, 8.0), 'European': (8.0, 14.5), 'US': (14.5, 21.0)} | |
| 44 | + | |
| 45 | + | |
| 46 | +def log(m): | |
| 47 | + print(f"[{time.time() - T0:6.1f}s] {m}", flush=True) | |
| 48 | + | |
| 49 | + | |
| 50 | +def load_5min_utc(sym): | |
| 51 | + df = pd.read_parquet(os.path.join(MINUTE_DIR, FILES[sym]), columns=['datetime', 'close']) | |
| 52 | + s = df.set_index('datetime')['close'].sort_index() | |
| 53 | + s = s.loc[START:END] | |
| 54 | + # FirstRate stamps are naive U.S. Eastern (bar-start convention); convert to UTC | |
| 55 | + idx = s.index.tz_localize('America/New_York', ambiguous='NaT', nonexistent='NaT') | |
| 56 | + s = s[~idx.isna()] | |
| 57 | + s.index = idx[~idx.isna()].tz_convert('UTC') | |
| 58 | + s5 = s.resample('5min').last().dropna() | |
| 59 | + r = np.log(s5).diff().dropna() | |
| 60 | + # drop returns spanning a gap longer than one hour (session breaks, weekends) | |
| 61 | + gaps = s5.index.to_series().diff().dt.total_seconds().reindex(r.index) | |
| 62 | + r = r[gaps <= 3600] | |
| 63 | + return r | |
| 64 | + | |
| 65 | + | |
| 66 | +rets = {} | |
| 67 | +for sym in FILES: | |
| 68 | + rets[sym] = load_5min_utc(sym) | |
| 69 | + log(f"{sym}: {len(rets[sym]):,} five-minute returns, {rets[sym].index.min().date()} -> {rets[sym].index.max().date()}") | |
| 70 | + | |
| 71 | +# ─── 1. Hourly profile (UTC) ────────────────────────────────────────────────── | |
| 72 | +hourly = pd.DataFrame({sym: r.abs().groupby(r.index.hour).mean() * 100 for sym, r in rets.items()}) | |
| 73 | +hourly.index.name = 'hour_utc' | |
| 74 | +hourly.to_csv(os.path.join(RESULTS, 'rev_intraday_hourly_absret_utc.csv'), float_format='%.5f') | |
| 75 | +hourly_et = pd.DataFrame({sym: r.abs().groupby(r.index.tz_convert('America/New_York').hour).mean() * 100 | |
| 76 | + for sym, r in rets.items()}) | |
| 77 | +hourly_et.index.name = 'hour_eastern' | |
| 78 | +hourly_et.to_csv(os.path.join(RESULTS, 'rev_intraday_hourly_absret_eastern.csv'), float_format='%.5f') | |
| 79 | + | |
| 80 | +fig, axes = plt.subplots(2, 2, figsize=(13, 7.5)) | |
| 81 | +for ax, sym in zip(axes.flatten(), ['VIX', 'ES', 'NQ', 'BTC']): | |
| 82 | + h = hourly[sym] | |
| 83 | + ax.bar(h.index, h.values, color=COLORS[sym], alpha=0.85, edgecolor='white', linewidth=0.5) | |
| 84 | + ax.axvspan(-0.5, 7.5, alpha=0.07, color='blue', label='Asian 00:00–08:00 UTC') | |
| 85 | + ax.axvspan(7.5, 14.0, alpha=0.07, color='green', label='European 08:00–14:30 UTC') | |
| 86 | + ax.axvspan(14.0, 20.5, alpha=0.07, color='orange', label='U.S. 14:30–21:00 UTC') | |
| 87 | + ax.set_title(f'{sym} — mean |5-min return| by hour (UTC)') | |
| 88 | + ax.set_xlabel('Hour of day (UTC)'); ax.set_ylabel('Mean |return| (%)') | |
| 89 | + ax.set_xticks(range(0, 24, 2)); ax.set_xlim(-0.6, 23.6) | |
| 90 | + if sym == 'VIX': | |
| 91 | + ax.legend(fontsize=7.5, loc='upper right') | |
| 92 | +plt.suptitle('Intraday periodicity of 5-minute absolute returns, 2016-03 to 2026-03 (time stamps converted from U.S. Eastern)', | |
| 93 | + fontsize=11) | |
| 94 | +plt.tight_layout() | |
| 95 | +for d in (FIGURES, PAPER_FIG): | |
| 96 | + fig.savefig(os.path.join(d, 'fig5_hourly_volatility.png'), dpi=150, bbox_inches='tight') | |
| 97 | +plt.close(fig) | |
| 98 | +log("hourly figure written") | |
| 99 | + | |
| 100 | +# ─── 2. Session realized variances per UTC day ──────────────────────────────── | |
| 101 | +def session_rv(r): | |
| 102 | + hour = r.index.hour + r.index.minute / 60 | |
| 103 | + day = r.index.tz_convert('UTC').normalize().tz_localize(None) | |
| 104 | + out = {} | |
| 105 | + for name, (a, b) in SESSIONS.items(): | |
| 106 | + m = (hour >= a) & (hour < b) | |
| 107 | + rv = (r[m] ** 2).groupby(day[m]).sum() | |
| 108 | + n = r[m].groupby(day[m]).size() | |
| 109 | + rv = rv[n >= 12] # at least one hour of bars | |
| 110 | + out[name] = rv | |
| 111 | + out['Day'] = (r ** 2).groupby(day).sum() | |
| 112 | + return pd.DataFrame(out) | |
| 113 | + | |
| 114 | + | |
| 115 | +sess = {sym: session_rv(r) for sym, r in rets.items()} | |
| 116 | +rows = [] | |
| 117 | +for sym, df in sess.items(): | |
| 118 | + wd = df[df.index.dayofweek < 5] | |
| 119 | + for name in SESSIONS: | |
| 120 | + s = wd[name].dropna() | |
| 121 | + rows.append({'Asset': sym, 'Session': name, 'Days': len(s), 'Ann_vol_pct': 100 * np.sqrt(252 * s).mean(), | |
| 122 | + 'Mean_absret_pct': np.nan, | |
| 123 | + 'Share_of_day_pct': 100 * (wd[name] / wd[['Asian', 'European', 'US']].sum(axis=1)).mean()}) | |
| 124 | +sess_tbl = pd.DataFrame(rows) | |
| 125 | +# mean absolute return per session | |
| 126 | +for sym, r in rets.items(): | |
| 127 | + hour = r.index.hour + r.index.minute / 60 | |
| 128 | + for name, (a, b) in SESSIONS.items(): | |
| 129 | + m = (hour >= a) & (hour < b) & (r.index.dayofweek < 5) | |
| 130 | + sess_tbl.loc[(sess_tbl.Asset == sym) & (sess_tbl.Session == name), 'Mean_absret_pct'] = 100 * r[m].abs().mean() | |
| 131 | +sess_tbl.to_csv(os.path.join(RESULTS, 'rev_intraday_sessions.csv'), index=False, float_format='%.4f') | |
| 132 | +log("session table done") | |
| 133 | + | |
| 134 | +# weekend share for BTC: average over ISO weeks of (Saturday + Sunday variance) / (weekly variance), | |
| 135 | +# which is robust to the extreme 2017 days; day-of-week profile as mean annualized daily RV | |
| 136 | +btc_day = sess['BTC']['Day'] | |
| 137 | +wk_var = btc_day.groupby(btc_day.index.to_period('W')).sum() | |
| 138 | +wk_end = btc_day[btc_day.index.dayofweek >= 5].groupby(btc_day[btc_day.index.dayofweek >= 5].index.to_period('W')).sum() | |
| 139 | +ratio = (wk_end / wk_var).dropna() | |
| 140 | +ratio = ratio[btc_day.groupby(btc_day.index.to_period('W')).size() == 7] | |
| 141 | +wk_share = ratio.mean() | |
| 142 | +btc_rv_day = 100 * np.sqrt(252 * btc_day) | |
| 143 | +btc_dow = btc_rv_day.groupby(btc_rv_day.index.dayofweek).mean() | |
| 144 | +btc_dow.to_csv(os.path.join(RESULTS, 'rev_intraday_btc_dayofweek.csv'), header=['ann_vol_pct']) | |
| 145 | +log(f"BTC weekend share of weekly variance: {100 * wk_share:.1f}%") | |
| 146 | + | |
| 147 | +# ─── 3. Session-ordered predictive regressions ─────────────────────────────── | |
| 148 | +def predictive(dep, pred_same_day=None, controls_lag=4, label=''): | |
| 149 | + """OLS of log dep RV on its own lags (+ optional same-day predictor and its lags); HAC Wald on predictor block.""" | |
| 150 | + df = pd.DataFrame({'y': np.log(dep.where(dep > 0))}) | |
| 151 | + X = [df['y'].shift(l).rename(f'y_l{l}') for l in range(1, controls_lag + 1)] | |
| 152 | + pred_cols = [] | |
| 153 | + if pred_same_day is not None: | |
| 154 | + x = np.log(pred_same_day.where(pred_same_day > 0)).reindex(df.index) | |
| 155 | + for l in range(0, controls_lag): | |
| 156 | + X.append(x.shift(l).rename(f'x_l{l}')) | |
| 157 | + pred_cols.append(f'x_l{l}') | |
| 158 | + X = sm.add_constant(pd.concat(X, axis=1)) | |
| 159 | + data = pd.concat([df['y'], X], axis=1).dropna() | |
| 160 | + m = sm.OLS(data['y'], data.drop(columns='y')).fit(cov_type='HAC', cov_kwds={'maxlags': 10}) | |
| 161 | + R = np.zeros((len(pred_cols), m.params.shape[0])) | |
| 162 | + for k, c in enumerate(pred_cols): | |
| 163 | + R[k, list(m.params.index).index(c)] = 1 | |
| 164 | + w = m.wald_test(R, use_f=False, scalar=True) | |
| 165 | + base = sm.OLS(data['y'], data.drop(columns=['y'] + pred_cols)).fit() | |
| 166 | + return {'Test': label, 'T': int(m.nobs), 'coef_x_l0': float(m.params['x_l0']), 'se_x_l0': float(m.bse['x_l0']), | |
| 167 | + 'Wald_HAC': float(w.statistic), 'p': float(w.pvalue), 'R2_with': m.rsquared, 'R2_without': base.rsquared} | |
| 168 | + | |
| 169 | + | |
| 170 | +wd = {sym: df[df.index.dayofweek < 5] for sym, df in sess.items()} | |
| 171 | +tests = [] | |
| 172 | +# (i) Bitcoin earlier sessions -> ES / NQ / VIX U.S. session (same day) | |
| 173 | +for tgt in ['ES', 'NQ', 'VIX']: | |
| 174 | + for s in ['Asian', 'European']: | |
| 175 | + tests.append(predictive(wd[tgt]['US'].dropna(), wd['BTC'][s], label=f'BTC {s} (t) $\\rightarrow$ {tgt} U.S. (t)')) | |
| 176 | +# (ii) ES / VIX U.S. session (t-1) -> Bitcoin Asian session (t): shift predictor by one day | |
| 177 | +for src in ['ES', 'NQ', 'VIX']: | |
| 178 | + prev = wd[src]['US'].dropna().copy() | |
| 179 | + prev.index = prev.index + pd.offsets.BDay(1) | |
| 180 | + tests.append(predictive(wd['BTC']['Asian'].dropna(), prev, label=f'{src} U.S. (t$-$1) $\\rightarrow$ BTC Asian (t)')) | |
| 181 | +# (iii) ES European (t) -> BTC U.S. (t) and BTC U.S. (t) -> ES U.S.(t) skipped: contemporaneous overlap | |
| 182 | +# (iv) ES Asian (Globex overnight, t) -> BTC U.S. (t) for symmetry | |
| 183 | +tests.append(predictive(wd['BTC']['US'].dropna(), wd['ES']['Asian'], label='ES Asian (t) $\\rightarrow$ BTC U.S. (t)')) | |
| 184 | +tests.append(predictive(wd['ES']['US'].dropna(), wd['ES']['Asian'], label='ES Asian (t) $\\rightarrow$ ES U.S. (t) [own overnight]')) | |
| 185 | +pred_df = pd.DataFrame(tests) | |
| 186 | +pred_df.to_csv(os.path.join(RESULTS, 'rev_intraday_session_predictive.csv'), index=False, float_format='%.4f') | |
| 187 | +log("session predictive regressions done") | |
| 188 | + | |
| 189 | +# (v) weekend Bitcoin variance -> Monday ES U.S.-session variance, controlling for Friday ES and Friday BTC | |
| 190 | +es_us = wd['ES']['US'].dropna() | |
| 191 | +mon = es_us[es_us.index.dayofweek == 0] | |
| 192 | +rows = [] | |
| 193 | +for d in mon.index: | |
| 194 | + fri = d - pd.Timedelta(days=3) | |
| 195 | + sat, sun = d - pd.Timedelta(days=2), d - pd.Timedelta(days=1) | |
| 196 | + bwk = btc_day.get(sat, np.nan) + btc_day.get(sun, np.nan) | |
| 197 | + rows.append({'date': d, 'es_mon': mon[d], 'es_fri': es_us.get(fri, np.nan), 'btc_wk': bwk, | |
| 198 | + 'btc_fri': btc_day.get(fri, np.nan), 'btc_mon_asia': wd['BTC']['Asian'].get(d, np.nan)}) | |
| 199 | +wk = pd.DataFrame(rows).set_index('date') | |
| 200 | +wk = np.log(wk.where(wk > 0)).dropna() | |
| 201 | +m1 = sm.OLS(wk['es_mon'], sm.add_constant(wk[['es_fri', 'btc_fri']])).fit(cov_type='HAC', cov_kwds={'maxlags': 4}) | |
| 202 | +m2 = sm.OLS(wk['es_mon'], sm.add_constant(wk[['es_fri', 'btc_fri', 'btc_wk']])).fit(cov_type='HAC', cov_kwds={'maxlags': 4}) | |
| 203 | +m3 = sm.OLS(wk['es_mon'], sm.add_constant(wk[['es_fri', 'btc_fri', 'btc_wk', 'btc_mon_asia']])).fit(cov_type='HAC', cov_kwds={'maxlags': 4}) | |
| 204 | +wk_res = pd.DataFrame({ | |
| 205 | + 'model': ['Friday controls only', '+ weekend BTC', '+ weekend BTC + Monday Asian BTC'], | |
| 206 | + 'N': [int(m1.nobs), int(m2.nobs), int(m3.nobs)], | |
| 207 | + 'coef_btc_wk': [np.nan, m2.params['btc_wk'], m3.params['btc_wk']], | |
| 208 | + 'se_btc_wk': [np.nan, m2.bse['btc_wk'], m3.bse['btc_wk']], | |
| 209 | + 'p_btc_wk': [np.nan, m2.pvalues['btc_wk'], m3.pvalues['btc_wk']], | |
| 210 | + 'coef_btc_mon_asia': [np.nan, np.nan, m3.params['btc_mon_asia']], | |
| 211 | + 'p_btc_mon_asia': [np.nan, np.nan, m3.pvalues['btc_mon_asia']], | |
| 212 | + 'coef_es_fri': [m1.params['es_fri'], m2.params['es_fri'], m3.params['es_fri']], | |
| 213 | + 'R2': [m1.rsquared, m2.rsquared, m3.rsquared]}) | |
| 214 | +wk_res.to_csv(os.path.join(RESULTS, 'rev_intraday_weekend_btc_monday_es.csv'), index=False, float_format='%.4f') | |
| 215 | +log("weekend regression done") | |
| 216 | + | |
| 217 | +# ─── 4. LaTeX tables ────────────────────────────────────────────────────────── | |
| 218 | +def fmt(x, d=2, sign=False): | |
| 219 | + if pd.isna(x): | |
| 220 | + return '--' | |
| 221 | + s = f"{x:+.{d}f}" if sign else f"{x:.{d}f}" | |
| 222 | + return s.replace('-', '$-$').replace('+', '$+$') if sign else s | |
| 223 | + | |
| 224 | + | |
| 225 | +def stars(p): | |
| 226 | + return r'$^{***}$' if p < 0.01 else r'$^{**}$' if p < 0.05 else r'$^{*}$' if p < 0.10 else '' | |
| 227 | + | |
| 228 | + | |
| 229 | +L = [r"\begin{tabular}{@{}llrrrr@{}}", r"\toprule", | |
| 230 | + r"Asset & Session (UTC) & Days & Mean $|r|$ (\%) & Annualized vol.\ (\%) & Share of day (\%) \\", r"\midrule"] | |
| 231 | +for sym in ['ES', 'NQ', 'VIX', 'BTC']: | |
| 232 | + sub = sess_tbl[sess_tbl.Asset == sym] | |
| 233 | + for k, (_, r) in enumerate(sub.iterrows()): | |
| 234 | + lab = {'Asian': 'Asian 00:00--08:00', 'European': 'European 08:00--14:30', 'US': 'U.S. 14:30--21:00'}[r['Session']] | |
| 235 | + L.append(f"{sym if k == 0 else ''} & {lab} & {int(r['Days'])} & {fmt(r['Mean_absret_pct'], 3)} & " | |
| 236 | + f"{fmt(r['Ann_vol_pct'], 1)} & {fmt(r['Share_of_day_pct'], 1)} \\\\") | |
| 237 | + if sym != 'BTC': | |
| 238 | + L.append(r"\addlinespace") | |
| 239 | +L += [r"\bottomrule", r"\end{tabular}"] | |
| 240 | +with open(os.path.join(TABLES, 'tab_sessions.tex'), 'w') as f: | |
| 241 | + f.write("\n".join(L)) | |
| 242 | + | |
| 243 | +L = [r"\begin{tabular}{@{}lrrrrr@{}}", r"\toprule", | |
| 244 | + r"Predictive relation & $T$ & Coef.\ (same day) & Wald (HAC) & $p$ & $\Delta R^2$ \\", r"\midrule"] | |
| 245 | +for _, r in pred_df.iterrows(): | |
| 246 | + L.append(f"{r['Test']} & {int(r['T'])} & {fmt(r['coef_x_l0'], 3, True)} ({fmt(r['se_x_l0'], 3)}) & " | |
| 247 | + f"{fmt(r['Wald_HAC'], 2)}{stars(r['p'])} & {fmt(r['p'], 3)} & {fmt(r['R2_with'] - r['R2_without'], 3)} \\\\") | |
| 248 | +L += [r"\bottomrule", r"\end{tabular}"] | |
| 249 | +with open(os.path.join(TABLES, 'tab_sessions_predictive.tex'), 'w') as f: | |
| 250 | + f.write("\n".join(L)) | |
| 251 | + | |
| 252 | +L = [r"\begin{tabular}{@{}lrrrrr@{}}", r"\toprule", | |
| 253 | + r"Specification & $N$ & $\ln \mathrm{RV}^{\mathrm{ES}}_{\mathrm{Fri}}$ & $\ln \mathrm{RV}^{\mathrm{BTC}}_{\mathrm{weekend}}$ & $\ln \mathrm{RV}^{\mathrm{BTC}}_{\mathrm{Mon,\,Asian}}$ & $R^2$ \\", | |
| 254 | + r"\midrule"] | |
| 255 | +for _, r in wk_res.iterrows(): | |
| 256 | + bw = '--' if pd.isna(r['coef_btc_wk']) else f"{fmt(r['coef_btc_wk'], 3, True)}{stars(r['p_btc_wk'])} ({fmt(r['se_btc_wk'], 3)})" | |
| 257 | + ba = '--' if pd.isna(r['coef_btc_mon_asia']) else f"{fmt(r['coef_btc_mon_asia'], 3, True)}{stars(r['p_btc_mon_asia'])}" | |
| 258 | + L.append(f"{r['model']} & {int(r['N'])} & {fmt(r['coef_es_fri'], 3, True)} & {bw} & {ba} & {fmt(r['R2'], 3)} \\\\") | |
| 259 | +L += [r"\bottomrule", r"\end{tabular}"] | |
| 260 | +with open(os.path.join(TABLES, 'tab_weekend_btc.tex'), 'w') as f: | |
| 261 | + f.write("\n".join(L)) | |
| 262 | + | |
| 263 | +key = {'btc_weekend_share_pct': 100 * wk_share} | |
| 264 | +for sym in FILES: | |
| 265 | + h = hourly[sym] | |
| 266 | + key[f'{sym}_peak_hour_utc'] = int(h.idxmax()); key[f'{sym}_peak_absret'] = h.max() | |
| 267 | + key[f'{sym}_min_hour_utc'] = int(h.idxmin()); key[f'{sym}_min_absret'] = h.min() | |
| 268 | + key[f'{sym}_peak_to_trough'] = h.max() / h.min() | |
| 269 | +for d, v in btc_dow.items(): | |
| 270 | + key[f'BTC_dow{d}_annvol'] = v | |
| 271 | +pd.Series(key).to_csv(os.path.join(RESULTS, 'rev_intraday_key_numbers.csv'), header=['value']) | |
| 272 | +print(pd.Series(key).to_string()) | |
| 273 | +print(sess_tbl.to_string()) | |
| 274 | +print(pred_df.to_string()) | |
| 275 | +print(wk_res.to_string()) | |
| 276 | +log("done") | |
| 277 | ||