harmonisation standard UQO WP (2026-10-17)

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

Simon-Pierre Boucher committed 2 h ago (Oct 17, 2026)

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	1	+# Raw & processed data — never committed (see data/raw/README.md for provenance)
	2	+data/raw/*
	3	+!data/raw/README.md
	4	+data/processed/*
	5	+!data/processed/.gitkeep
	6	+
	7	+# Python
	8	+__pycache__/
	9	+*.pyc
	10	+.pytest_cache/
	11	+.venv/
	12	+*.egg-info/
	13	+
	14	+# LaTeX build artifacts (paper/main.pdf IS committed)
	15	+paper/*.aux
	16	+paper/*.log
	17	+paper/*.out
	18	+paper/*.toc
	19	+paper/*.lof
	20	+paper/*.lot
	21	+paper/*.fls
	22	+paper/*.fdb_latexmk
	23	+paper/*.bbl
	24	+paper/*.blg
	25	+paper/*.spl
	26	+paper/*.synctex.gz
	27	+paper/*.run.xml
	28	+paper/*.bcf
	29	+
	30	+# Logs
	31	+logs/
	32	+*.log
	33	+
	34	+# macOS
	35	+.DS_Store
	36	+
	37	+# Raw 5-minute OHLCV DuckDB databases (several GB) — not redistributed
	38	+*.duckdb

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	1	+<!-- Author: Simon-Pierre Boucher — simon-pierre.boucher@uqo.ca -->
	2	+# 🌐 Intraday Volatility Transmission Across Asset Classes
	3	+
	4	+UQO Working Paper No. 6 — A Connectedness Analysis of Equities, Fixed Income, Commodities, and Cryptocurrencies
	5	+
	6	+[![Paper](https://img.shields.io/badge/paper-PDF%20(31%20p.)-b31b1b?logo=latex&logoColor=white)](paper/main.pdf)
	7	+[![Python](https://img.shields.io/badge/python-3.11%2B-3776AB?logo=python&logoColor=white)](requirements.txt)
	8	+[![Data](https://img.shields.io/badge/data-235M%205--min%20bars%20·%2010%20instruments%20·%20DuckDB-4051b5)](data/raw/README.md)
	9	+[![Reproducible](https://img.shields.io/badge/reproducible-end--to--end%20pipeline-2e7d32)](scripts/)
	10	+[![Institution](https://img.shields.io/badge/UQO-D%C3%A9pt.%20des%20sciences%20administratives-16365c)](https://uqo.ca)
	11	+[![Author](https://img.shields.io/badge/author-Simon--Pierre%20Boucher-16365c)](mailto:simon-pierre.boucher@uqo.ca)
	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).
	14	+
	15	+---
	16	+
	17	+## 📌 Status
	18	+
	19	+\| Item \| Value \|
	20	+\|---\|---\|
	21	+\| Version \| 1.0 (May 2026) \|
	22	+\| SSRN \| not yet submitted \|
	23	+\| Journal \| — \|
	24	+\| Code & data \| reproducible from `scripts/01_analysis.py`; raw DuckDB files not redistributed \|
	25	+
	26	+## 🎯 What this paper does
	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:
	29	+
	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
	32	+```
	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.
	35	+
	36	+## 🏆 Headline results
	37	+
	38	+\| Object \| Estimate \|
	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 \|
	48	+
	49	+## 🗂 Repository layout
	50	+
	51	+```
	52	+intraday-volatility-connectedness/
	53	+├── data/
	54	+│ ├── raw/ # futures_5min / fx_5min / crypto_5min .duckdb (see data/raw/README.md) — not committed
	55	+│ └── processed/
	56	+├── 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
	61	+```
	62	+
	63	+## 🚀 Quick start
	64	+
	65	+```bash
	66	+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)
	69	+cd paper && make # latexmk → main.pdf
	70	+```
	71	+
	72	+## 🗃 Data
	73	+
	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`.
	75	+
	76	+## 🔬 Methodology
	77	+
	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).
	84	+
	85	+## 🖼 Figures & tables inventory
	86	+
	87	+\| Figure \| Content \|
	88	+\|---\|---\|
	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 \|
	96	+
	97	+Tables (`results/*.csv`): descriptive statistics, full connectedness table, three regime tables, session Granger tests.
	98	+
	99	+## ⚠️ Limitations
	100	+
	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.
	104	+
	105	+## 📝 Citation
	106	+
	107	+```bibtex
	108	+@techreport{boucher2026connectedness,
	109	+ author = {Boucher, Simon-Pierre},
	110	+ title = {Intraday Volatility Transmission Across Asset Classes: A Connectedness Analysis of Equities, Fixed Income, Commodities, and Cryptocurrencies},
	111	+ institution = {Universit\'e du Qu\'ebec en Outaouais, D\'epartement des sciences administratives},
	112	+ type = {Working Paper},
	113	+ number = {6},
	114	+ year = {2026},
	115	+ month = {May}
	116	+}
	117	+```
	118	+
	119	+## 👤 Author & contact
	120	+
	121	+Simon-Pierre Boucher — Département des sciences administratives,
	122	+Université du Québec en Outaouais (UQO), Gatineau, QC.
	123	+📧 [simon-pierre.boucher@uqo.ca](mailto:simon-pierre.boucher@uqo.ca)
	124	+
	125	+## 🗒 Notes
	126	+
	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).
	128	+- 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	+# Raw data — WP 6
	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)`:
	4	+
	5	+\| File \| Symbols used \| Source \|
	6	+\|---\|---\|---\|
	7	+\| `futures_5min.duckdb` \| ES, NQ, GC, CL, VX (VIX futures) \| FirstRate Data (CME/CBOE futures, continuous contracts) \|
	8	+\| `fx_5min.duckdb` \| EURUSD, USDJPY, GBPUSD \| FirstRate Data (spot FX) \|
	9	+\| `crypto_5min.duckdb` \| BTC, ETH \| FirstRate Data (crypto spot, USD) \|
	10	+
	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/`.

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	1	+$pdf_mode = 1;
	2	+$pdflatex = 'pdflatex -interaction=nonstopmode -halt-on-error -synctex=1 %O %S';
	3	+$bibtex_use = 2;
	4	+$clean_ext = 'synctex.gz run.xml bbl bcf fdb_latexmk fls log aux out toc lof lot blg';
	5	+@default_files = ('main.tex');

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	1	+.PHONY: all clean distclean
	2	+
	3	+all:
	4	+ latexmk
	5	+
	6	+clean:
	7	+ latexmk -c
	8	+
	9	+distclean:
	10	+ latexmk -C
	11	+ rm -f .synctex.gz .run.xml .bbl .bcf

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	1	+\section{Robustness Checks}
	2	+\label{sec:robustness}
	3	+
	4	+\subsection{Sensitivity to VAR Lag Selection}
	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 $p \in \{2, 4, 6\}$.
	7	+
	8	+\begin{table}[htbp]
	9	+\centering
	10	+\caption{Robustness to VAR Lag Selection.}
	11	+\label{tab:robustness_lags}
	12	+\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}
	23	+\begin{tablenotes}[flushleft]
	24	+\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.
	26	+\end{tablenotes}
	27	+\end{threeparttable}
	28	+\end{table}
	29	+
	30	+\subsection{Sensitivity to Forecast Horizon}
	31	+
	32	+\Cref{tab:robustness_horizon} reports sensitivity to the forecast horizon $H$.
	33	+
	34	+\begin{table}[htbp]
	35	+\centering
	36	+\caption{Robustness to Forecast Horizon.}
	37	+\label{tab:robustness_horizon}
	38	+\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}
	48	+\begin{tablenotes}[flushleft]
	49	+\footnotesize
	50	+\item \textit{Notes:} Cross-asset spillovers increase with the horizon, as expected, but qualitative conclusions regarding the volatility hierarchy are robust.
	51	+\end{tablenotes}
	52	+\end{threeparttable}
	53	+\end{table}
	54	+
	55	+\newpage
	56	+\section{Summary of Key Numerical Results}
	57	+\label{sec:appendix_summary}
	58	+
	59	+\begin{table}[htbp]
	60	+\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}
	97	+\end{table}

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	1	+% ============================================================================
	2	+% UQO Working Paper No. 6
	3	+% Intraday Volatility Transmission Across Asset Classes:
	4	+% A Connectedness Analysis of Equities, Fixed Income, Commodities,
	5	+% and Cryptocurrencies
	6	+% ============================================================================
	7	+\documentclass[12pt,letterpaper]{article}
	8	+
	9	+% --- Encoding & Language ---
	10	+\usepackage[utf8]{inputenc}
	11	+\usepackage[T1]{fontenc}
	12	+\usepackage[english]{babel}
	13	+
	14	+% --- Page Layout ---
	15	+\usepackage[
	16	+ letterpaper,
	17	+ top=1in, bottom=1in, left=1in, right=1in,
	18	+ headheight=15pt
	19	+]{geometry}
	20	+\usepackage{setspace}
	21	+\onehalfspacing
	22	+
	23	+% --- Typography ---
	24	+\usepackage{newtxtext,newtxmath}
	25	+\usepackage{microtype}
	26	+
	27	+% --- Math ---
	28	+\usepackage{amsmath}
	29	+\let\Bbbk\relax
	30	+\usepackage{amssymb,amsfonts}
	31	+\usepackage{mathtools}
	32	+
	33	+% --- Tables ---
	34	+\usepackage{booktabs}
	35	+\usepackage{tabularx}
	36	+\usepackage{multirow}
	37	+\usepackage{threeparttable}
	38	+\usepackage{array}
	39	+\usepackage{adjustbox}
	40	+\usepackage{longtable}
	41	+\usepackage{dcolumn}
	42	+\newcolumntype{d}[1]{D{.}{.}{#1}}
	43	+
	44	+% --- Figures ---
	45	+\usepackage{graphicx}
	46	+\usepackage{float}
	47	+\usepackage[
	48	+ font = small,
	49	+ labelfont = bf,
	50	+ labelsep = period,
	51	+ skip = 6pt,
	52	+ justification = justified,
	53	+ singlelinecheck = false
	54	+]{caption}
	55	+\usepackage{subcaption}
	56	+
	57	+% --- Lists ---
	58	+\usepackage{enumitem}
	59	+\setlist{nosep,leftmargin=*}
	60	+
	61	+% --- Colors & Links ---
	62	+\usepackage[dvipsnames,table]{xcolor}
	63	+\usepackage[bookmarks, bookmarksnumbered]{hyperref}
	64	+\hypersetup{
	65	+ colorlinks = true,
	66	+ linkcolor = NavyBlue,
	67	+ citecolor = NavyBlue,
	68	+ urlcolor = NavyBlue,
	69	+ 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}
	73	+}
	74	+\usepackage{cleveref}
	75	+
	76	+% --- Landscape & Rotation ---
	77	+\usepackage{pdflscape}
	78	+\usepackage{rotating}
	79	+
	80	+% --- Bibliography ---
	81	+\usepackage{natbib}
	82	+\setcitestyle{authoryear,round,semicolon}
	83	+\bibliographystyle{apalike}
	84	+
	85	+% --- Headers & Footers ---
	86	+\usepackage{fancyhdr}
	87	+\pagestyle{fancy}
	88	+\fancyhf{}
	89	+\fancyhead[L]{\small\itshape Intraday Volatility Transmission}
	90	+\fancyhead[R]{\small\thepage}
	91	+\renewcommand{\headrulewidth}{0.4pt}
	92	+\renewcommand{\footrulewidth}{0pt}
	93	+\fancypagestyle{plain}{%
	94	+ \fancyhf{}
	95	+ \fancyfoot[C]{\small\thepage}
	96	+ \renewcommand{\headrulewidth}{0pt}
	97	+}
	98	+
	99	+% --- Section Formatting ---
	100	+\usepackage{titlesec}
	101	+\titleformat{\section}{\large\bfseries}{\thesection.}{0.5em}{}
	102	+\titleformat{\subsection}{\normalsize\bfseries}{\thesubsection.}{0.5em}{}
	103	+\titleformat{\subsubsection}{\normalsize\itshape}{\thesubsubsection.}{0.5em}{}
	104	+\titlespacing*{\section}{0pt}{18pt}{8pt}
	105	+\titlespacing*{\subsection}{0pt}{12pt}{4pt}
	106	+\titlespacing*{\subsubsection}{0pt}{10pt}{3pt}
	107	+
	108	+% --- Footnotes ---
	109	+\usepackage[bottom,hang]{footmisc}
	110	+\setlength{\footnotemargin}{0.5em}
	111	+
	112	+% --- Appendix ---
	113	+\usepackage{apptools}
	114	+\AtAppendix{%
	115	+ \renewcommand{\thetable}{A\arabic{table}}%
	116	+ \setcounter{table}{0}%
	117	+ \renewcommand{\thefigure}{A\arabic{figure}}%
	118	+ \setcounter{figure}{0}%
	119	+ \renewcommand{\theequation}{A.\arabic{equation}}%
	120	+ \setcounter{equation}{0}%
	121	+}
	122	+
	123	+% --- Graphics Path ---
	124	+\graphicspath{{figures/}}
	125	+
	126	+% --- Custom Commands ---
	127	+\newcommand{\RV}{\mathrm{RV}}
	128	+\newcommand{\GFEVD}{\mathrm{GFEVD}}
	129	+\newcommand{\TSI}{\mathrm{TSI}}
	130	+\newcommand{\ie}{\textit{i.e.}}
	131	+\newcommand{\eg}{\textit{e.g.}}
	132	+\newcommand{\etal}{\textit{et al.}}
	133	+
	134	+% --- Significance Stars ---
	135	+\newcommand{\sym}[1]{\ensuremath{^{#1}}}
	136	+\newcommand{\stmark}{\sym{***}}
	137	+\newcommand{\smark}{\sym{**}}
	138	+\newcommand{\tmark}{\sym{*}}
	139	+
	140	+% ============================================================================
	141	+% METADATA
	142	+% ============================================================================
	143	+\newcommand{\WPnumber}{6}
	144	+\newcommand{\WPtitle}{Intraday Volatility Transmission Across Asset Classes: A Connectedness Analysis of Equities, Fixed Income, Commodities, and Cryptocurrencies}
	145	+\newcommand{\WPsubtitle}{}
	146	+\newcommand{\WPdate}{May 2026}
	147	+\newcommand{\WPversion}{1.0}
	148	+\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	+}
	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}
	153	+
	154	+% --- Author ---
	155	+\newcommand{\WPauthor}{Simon-Pierre Boucher}
	156	+\newcommand{\WPaffiliation}{%
	157	+ D\'epartement des sciences administratives\\
	158	+ Universit\'e du Qu\'ebec en Outaouais%
	159	+}
	160	+\newcommand{\WPemail}{simon-pierre.boucher@uqo.ca}
	161	+\newcommand{\WPaddress}{%
	162	+ Gatineau -- Pavillon Alexandre-Tach\'e\\
	163	+ 283, boulevard Alexandre-Tach\'e\\
	164	+ Gatineau, Qu\'ebec, Canada J9A 1L8%
	165	+}
	166	+
	167	+% ============================================================================
	168	+% DOCUMENT
	169	+% ============================================================================
	170	+\begin{document}
	171	+
	172	+% --- Title Page ---
	173	+\input{sections/titlepage}
	174	+
	175	+% --- Table of Contents ---
	176	+\setcounter{page}{1}
	177	+\tableofcontents
	178	+\newpage
	179	+
	180	+% --- Main Body ---
	181	+\input{sections/introduction}
	182	+\input{sections/literature}
	183	+\input{sections/methodology}
	184	+\input{sections/data}
	185	+\input{sections/results}
	186	+\input{sections/discussion}
	187	+\input{sections/conclusion}
	188	+
	189	+% --- References ---
	190	+\input{sections/references}
	191	+
	192	+% --- Appendix ---
	193	+\newpage
	194	+\appendix
	195	+\input{appendix/appendix}
	196	+
	197	+\end{document}

added paper/sections/conclusion.tex +14 −0

		`@@ -0,0 +1,14 @@`
	1	+% ============================================================================
	2	+\section{Conclusion}
	3	+\label{sec:conclusion}
	4	+% ============================================================================
	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.
	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.
	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.
	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.

added paper/sections/data.tex +91 −0

		`@@ -0,0 +1,91 @@`
	1	+% ============================================================================
	2	+\section{Data}
	3	+\label{sec:data}
	4	+% ============================================================================
	5	+
	6	+\subsection{Data Sources and Description}
	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.
	9	+
	10	+\begin{table}[htbp]
	11	+\centering
	12	+\caption{Asset Universe.}
	13	+\label{tab:asset_universe}
	14	+\begin{threeparttable}
	15	+\begin{tabular}{@{}llll@{}}
	16	+\toprule
	17	+Asset Class & Symbol & Description & Source \\
	18	+\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 \\
	29	+\bottomrule
	30	+\end{tabular}
	31	+\begin{tablenotes}[flushleft]
	32	+\footnotesize
	33	+\item \textit{Notes:} All data are 5-minute OHLCV bars stored in DuckDB databases. Source column indicates the database of origin.
	34	+\end{tablenotes}
	35	+\end{threeparttable}
	36	+\end{table}
	37	+
	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	+
	40	+\subsection{Descriptive Statistics of Intraday Returns}
	41	+
	42	+\Cref{tab:descriptive_stats} presents descriptive statistics for 5-minute log returns across all 10 assets.
	43	+
	44	+\begin{table}[htbp]
	45	+\centering
	46	+\caption{Descriptive Statistics of 5-Minute Log Returns.}
	47	+\label{tab:descriptive_stats}
	48	+\begin{threeparttable}
	49	+\begin{adjustbox}{max width=\textwidth}
	50	+\begin{tabular}{@{}llr@{\quad}l@{\quad}lrrrr@{\quad}r@{}}
	51	+\toprule
	52	+Asset & Class & $N$ (M) & Start & End & Std (\%) & Skew & Kurt & Min (\%) & Max (\%) \\
	53	+\midrule
	54	+ES & Equity & 1.28 & 2008-01 & 2026-03 & 0.073 & $-0.05$ & 35.3 & $-1.50$ & 1.50 \\
	55	+NQ & Equity & 1.28 & 2008-01 & 2026-03 & 0.084 & $-0.03$ & 30.1 & $-1.70$ & 1.70 \\
	56	+EURUSD & FX & 1.21 & 2010-01 & 2026-03 & 0.032 & $+0.12$ & 20.4 & $-0.63$ & 0.64 \\
	57	+USDJPY & FX & 1.20 & 2010-01 & 2026-03 & 0.034 & $-0.12$ & 27.7 & $-0.70$ & 0.70 \\
	58	+GBPUSD & FX & 1.20 & 2010-01 & 2026-03 & 0.033 & $+0.09$ & 21.8 & $-0.69$ & 0.69 \\
	59	+GC & Commodity & 1.29 & 2008-01 & 2026-03 & 0.067 & $-0.20$ & 25.3 & $-1.36$ & 1.36 \\
	60	+CL & Commodity & 1.29 & 2008-01 & 2026-03 & 0.150 & $-0.14$ & 38.2 & $-3.28$ & 3.35 \\
	61	+BTC & Crypto & 1.32 & 2013-04 & 2026-03 & 0.648 & $+0.02$ & 55.5 & $-14.90$ & 14.84 \\
	62	+ETH & Crypto & 1.01 & 2016-03 & 2026-03 & 0.597 & $+0.03$ & 63.0 & $-12.66$ & 12.73 \\
	63	+VIX & Volatility & 0.55 & 2008-01 & 2026-03 & 0.688 & $+1.00$ & 52.6 & $-14.58$ & 14.65 \\
	64	+\bottomrule
	65	+\end{tabular}
	66	+\end{adjustbox}
	67	+\begin{tablenotes}[flushleft]
	68	+\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 $N$.
	70	+\end{tablenotes}
	71	+\end{threeparttable}
	72	+\end{table}
	73	+
	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}
	77	+
	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.
	79	+
	80	+\begin{figure}[htbp]
	81	+\centering
	82	+\includegraphics[width=\textwidth]{fig1_rv_timeseries.png}
	83	+\caption{Daily Realized Volatility Time Series (Annualized, 5-Minute Frequency).}
	84	+\label{fig:rv_timeseries}
	85	+\begin{minipage}{0.95\textwidth}
	86	+\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.
	88	+\end{minipage}
	89	+\end{figure}
	90	+
	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\%).

added paper/sections/discussion.tex +24 −0

		`@@ -0,0 +1,24 @@`
	1	+% ============================================================================
	2	+\section{Discussion}
	3	+\label{sec:discussion}
	4	+% ============================================================================
	5	+
	6	+\subsection{Addressing the Research Questions}
	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.
	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.''
	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.
	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.
	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.
	17	+
	18	+\subsection{Implications for Portfolio Construction and Risk Management}
	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.
	21	+
	22	+\subsection{Limitations}
	23	+
	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.

added paper/sections/introduction.tex +24 −0

		`@@ -0,0 +1,24 @@`
	1	+% ============================================================================
	2	+\section{Introduction}
	3	+\label{sec:introduction}
	4	+% ============================================================================
	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.
	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}.
	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.
	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:
	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}
	21	+
	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.
	23	+
	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.

added paper/sections/literature.tex +40 −0

		`@@ -0,0 +1,40 @@`
	1	+% ============================================================================
	2	+\section{Literature Review}
	3	+\label{sec:literature}
	4	+% ============================================================================
	5	+
	6	+\subsection{Volatility Spillovers and Connectedness}
	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.
	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.
	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.
	13	+
	14	+\subsection{Cross-Asset Volatility Transmission}
	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.
	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}.
	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.
	21	+
	22	+\subsection{Cryptocurrency and Traditional Market Integration}
	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.
	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.
	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.
	29	+
	30	+\subsection{Intraday Volatility Dynamics and Trading Sessions}
	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.
	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}.
	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.

added paper/sections/methodology.tex +115 −0

		`@@ -0,0 +1,115 @@`
	1	+% ============================================================================
	2	+\section{Methodology}
	3	+\label{sec:methodology}
	4	+% ============================================================================
	5	+
	6	+\subsection{Realized Volatility}
	7	+
	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	+\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.
	17	+ \label{eq:rv}
	18	+\end{equation}
	19	+
	20	+The annualized daily realized volatility is then:
	21	+\begin{equation}
	22	+ \sigma_{i,t}^{\RV} = \sqrt{252 \cdot \RV_{i,t}}.
	23	+ \label{eq:rv_annualized}
	24	+\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:
	27	+\begin{equation}
	28	+ \RV_{i,t} \xrightarrow{p} \int_0^1 \sigma_{i,t}^2(s)\, ds.
	29	+ \label{eq:rv_convergence}
	30	+\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}.
	33	+
	34	+\subsection{Vector Autoregression}
	35	+
	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:
	37	+\begin{equation}
	38	+ \mathbf{y}_t = \boldsymbol{\mu} + \sum_{\ell=1}^{p} \boldsymbol{\Phi}_\ell \mathbf{y}_{t-\ell} + \boldsymbol{\varepsilon}_t,
	39	+ \label{eq:var}
	40	+\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:
	42	+\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
	49	+ \label{eq:psi_recursion}
	50	+\end{equation}
	51	+with $\boldsymbol{\Psi}_0 = \mathbf{I}_N$ and $\boldsymbol{\Phi}_\ell = \mathbf{0}$ for $\ell > p$.
	52	+
	53	+\subsection{Generalized Forecast Error Variance Decomposition}
	54	+
	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:
	56	+\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},
	58	+ \label{eq:gfevd}
	59	+\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:
	61	+\begin{equation}
	62	+ \tilde{\theta}_{ij}^g(H) = \frac{\theta_{ij}^g(H)}{\sum_{j=1}^{N} \theta_{ij}^g(H)},
	63	+ \label{eq:gfevd_normalized}
	64	+\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}
	68	+
	69	+From the normalized GFEVD matrix $\tilde{\boldsymbol{\Theta}}^g(H) = [\tilde{\theta}_{ij}^g(H)]$, we define four spillover measures.
	70	+
	71	+\paragraph{Total Spillover Index.}
	72	+\begin{equation}
	73	+ \TSI(H) = \frac{\sum_{\substack{i,j=1 \\ i \neq j}}^{N} \tilde{\theta}_{ij}^g(H)}{N} \times 100.
	74	+ \label{eq:tsi}
	75	+\end{equation}
	76	+
	77	+\paragraph{Directional Spillovers TO Others.} The volatility spillover transmitted by market $j$ to all other markets:
	78	+\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}
	81	+\end{equation}
	82	+
	83	+\paragraph{Directional Spillovers FROM Others.} The volatility spillover received by market $i$ from all other markets:
	84	+\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}
	87	+\end{equation}
	88	+
	89	+\paragraph{Net Directional Spillovers.} The net volatility spillover for market $i$:
	90	+\begin{equation}
	91	+ S_i^{\text{net}}(H) = S_{\cdot i}^g(H) - S_{i \cdot}^g(H).
	92	+ \label{eq:net_spillover}
	93	+\end{equation}
	94	+A positive (negative) value indicates that market $i$ is a net transmitter (receiver) of volatility.
	95	+
	96	+\subsection{Rolling Window Analysis}
	97	+
	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:
	99	+\begin{equation}
	100	+ \TSI_t(H) = \TSI(H; \mathbf{y}_{t-w+1}, \ldots, \mathbf{y}_t).
	101	+ \label{eq:rolling_tsi}
	102	+\end{equation}
	103	+
	104	+\subsection{Granger Causality Tests}
	105	+
	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:
	107	+\begin{equation}
	108	+ F = \frac{(\text{RSS}_R - \text{RSS}_U) / p}{\text{RSS}_U / (T - 2p - 1)},
	109	+ \label{eq:granger_f}
	110	+\end{equation}
	111	+where $\text{RSS}_R$ and $\text{RSS}_U$ are the residual sums of squares from the restricted and unrestricted models.
	112	+
	113	+\subsection{Network Representation}
	114	+
	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.

added paper/sections/references.tex +236 −0

		`@@ -0,0 +1,236 @@`
	1	+% ============================================================================
	2	+% REFERENCES
	3	+% ============================================================================
	4	+\newpage
	5	+\phantomsection
	6	+\addcontentsline{toc}{section}{References}
	7	+\bibliographystyle{apalike}
	8	+
	9	+\begin{thebibliography}{99}
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added paper/sections/results.tex +301 −0

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	1	+% ============================================================================
	2	+\section{Empirical Results}
	3	+\label{sec:results}
	4	+% ============================================================================
	5	+
	6	+\subsection{Full-Sample Connectedness Analysis}
	7	+
	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	+
	10	+\begin{table}[htbp]
	11	+\centering
	12	+\caption{Full-Sample Diebold--Yilmaz Connectedness Table.}
	13	+\label{tab:connectedness_full}
	14	+\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}
	38	+\begin{tablenotes}[flushleft]
	39	+\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.
	41	+\end{tablenotes}
	42	+\end{threeparttable}
	43	+\end{table}
	44	+
	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:
	46	+
	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.
	48	+
	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.
	50	+
	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.
	52	+
	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).
	54	+
	55	+\Cref{fig:connectedness_heatmap} provides a visual representation of the connectedness matrix.
	56	+
	57	+\begin{figure}[htbp]
	58	+\centering
	59	+\includegraphics[width=0.85\textwidth]{fig2_connectedness_heatmap.png}
	60	+\caption{Diebold--Yilmaz Connectedness Heatmap (Full Sample).}
	61	+\label{fig:connectedness_heatmap}
	62	+\begin{minipage}{0.95\textwidth}
	63	+\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.
	65	+\end{minipage}
	66	+\end{figure}
	67	+
	68	+\subsection{Time-Varying Connectedness}
	69	+
	70	+\Cref{fig:rolling_spillover} presents the rolling 200-day total spillover index over the 2016--2026 period.
	71	+
	72	+\begin{figure}[htbp]
	73	+\centering
	74	+\includegraphics[width=\textwidth]{fig3_rolling_spillover.png}
	75	+\caption{Rolling 200-Day Total Spillover Index with Event Markers.}
	76	+\label{fig:rolling_spillover}
	77	+\begin{minipage}{0.95\textwidth}
	78	+\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).
	80	+\end{minipage}
	81	+\end{figure}
	82	+
	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}
	92	+
	93	+\subsection{Regime-Specific Connectedness}
	94	+
	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)}
	98	+
	99	+\begin{table}[htbp]
	100	+\centering
	101	+\caption{Connectedness Table --- Pre-COVID Regime (2019-01 to 2020-02).}
	102	+\label{tab:connectedness_precovid}
	103	+\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}
	125	+\begin{tablenotes}[flushleft]
	126	+\footnotesize
	127	+\item \textit{Notes:} Same methodology as \Cref{tab:connectedness_full}. TSI = 64.72\%.
	128	+\end{tablenotes}
	129	+\end{threeparttable}
	130	+\end{table}
	131	+
	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.
	133	+
	134	+\subsubsection{COVID Crash Regime (March--June 2020)}
	135	+
	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 & $-$16.1 & \\
	159	+\bottomrule
	160	+\end{tabular}
	161	+\end{adjustbox}
	162	+\begin{tablenotes}[flushleft]
	163	+\footnotesize
	164	+\item \textit{Notes:} Same methodology as \Cref{tab:connectedness_full}. TSI = 66.66\%.
	165	+\end{tablenotes}
	166	+\end{threeparttable}
	167	+\end{table}
	168	+
	169	+The COVID crash regime reveals a dramatic restructuring of the volatility hierarchy. USDJPY emerges as the dominant volatility transmitter ($+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.
	170	+
	171	+\subsubsection{Rate-Hiking Regime (January--December 2022)}
	172	+
	173	+\begin{table}[htbp]
	174	+\centering
	175	+\caption{Connectedness Table --- Rate-Hiking Regime (2022-01 to 2022-12).}
	176	+\label{tab:connectedness_ratehikes}
	177	+\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 & $-$8.5 & \\
	196	+\bottomrule
	197	+\end{tabular}
	198	+\end{adjustbox}
	199	+\begin{tablenotes}[flushleft]
	200	+\footnotesize
	201	+\item \textit{Notes:} Same methodology as \Cref{tab:connectedness_full}. TSI = 65.62\%.
	202	+\end{tablenotes}
	203	+\end{threeparttable}
	204	+\end{table}
	205	+
	206	+The 2022 regime reveals that \textbf{BTC transitions to a net volatility transmitter} ($+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	+\begin{figure}[htbp]
	211	+\centering
	212	+\includegraphics[width=\textwidth]{fig4_net_spillovers_regimes.png}
	213	+\caption{Net Directional Spillovers by Market Regime.}
	214	+\label{fig:net_spillovers_regimes}
	215	+\begin{minipage}{0.95\textwidth}
	216	+\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.
	218	+\end{minipage}
	219	+\end{figure}
	220	+
	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.
	224	+
	225	+\begin{figure}[htbp]
	226	+\centering
	227	+\includegraphics[width=\textwidth]{fig6_net_directional_btc_es.png}
	228	+\caption{Rolling Net Directional Spillovers: BTC vs.\ ES.}
	229	+\label{fig:net_directional_btc_es}
	230	+\begin{minipage}{0.95\textwidth}
	231	+\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.
	233	+\end{minipage}
	234	+\end{figure}
	235	+
	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.
	237	+
	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\%).
	241	+
	242	+\begin{figure}[htbp]
	243	+\centering
	244	+\includegraphics[width=0.85\textwidth]{fig7_network_graph.png}
	245	+\caption{Volatility Transmission Network.}
	246	+\label{fig:network_graph}
	247	+\begin{minipage}{0.95\textwidth}
	248	+\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.
	250	+\end{minipage}
	251	+\end{figure}
	252	+
	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.
	254	+
	255	+\subsection{Trading Session Analysis}
	256	+
	257	+\Cref{fig:hourly_volatility} displays the average absolute 5-minute return by hour of day (UTC) for VIX, ES, NQ, and BTC.
	258	+
	259	+\begin{figure}[htbp]
	260	+\centering
	261	+\includegraphics[width=\textwidth]{fig5_hourly_volatility.png}
	262	+\caption{Intraday Volatility Pattern by Asset and Trading Session.}
	263	+\label{fig:hourly_volatility}
	264	+\begin{minipage}{0.95\textwidth}
	265	+\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.
	267	+\end{minipage}
	268	+\end{figure}
	269	+
	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.
	273	+
	274	+\begin{table}[htbp]
	275	+\centering
	276	+\caption{Granger Causality Tests for Realized Volatility.}
	277	+\label{tab:granger_causality}
	278	+\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}
	294	+\begin{tablenotes}[flushleft]
	295	+\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.
	297	+\end{tablenotes}
	298	+\end{threeparttable}
	299	+\end{table}
	300	+
	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.

added paper/sections/titlepage.tex +77 −0

		`@@ -0,0 +1,77 @@`
	1	+% ============================================================================
	2	+% Title Page
	3	+% ============================================================================
	4	+\thispagestyle{empty}
	5	+
	6	+\begin{center}
	7	+
	8	+% --- Logo ---
	9	+\includegraphics[width=3.5cm]{uq_logo.jpg}
	10	+
	11	+\vspace{0.6cm}
	12	+
	13	+{\footnotesize\textsc{Université du Québec en Outaouais}}\\[0.15cm]
	14	+{\footnotesize\textsc{Département des sciences administratives}}
	15	+
	16	+\vspace{0.8cm}
	17	+
	18	+{\footnotesize\textsc{Working Paper No.~\WPnumber}}
	19	+
	20	+\vspace{1.2cm}
	21	+
	22	+% --- Title ---
	23	+{\LARGE\bfseries \WPtitle\par}
	24	+
	25	+\ifx\WPsubtitle\empty\else
	26	+ \vspace{0.3cm}
	27	+ {\large\itshape \WPsubtitle\par}
	28	+\fi
	29	+
	30	+\vspace{1.2cm}
	31	+
	32	+% --- Author ---
	33	+{\large \WPauthor}\\[0.3cm]
	34	+{\normalsize \WPaffiliation}\\[0.15cm]
	35	+{\normalsize \href{mailto:\WPemail}{\WPemail}}\\[0.15cm]
	36	+{\small \WPaddress}
	37	+
	38	+\vspace{0.8cm}
	39	+
	40	+% --- Date & Version ---
	41	+{\normalsize \WPdate}\\[0.1cm]
	42	+{\small Version~\WPversion}
	43	+
	44	+\end{center}
	45	+
	46	+\vfill
	47	+
	48	+\newpage
	49	+
	50	+% ============================================================================
	51	+% Abstract Page
	52	+% ============================================================================
	53	+\thispagestyle{empty}
	54	+
	55	+\vspace*{1cm}
	56	+
	57	+\noindent\rule{\textwidth}{0.4pt}
	58	+\vspace{0.3cm}
	59	+
	60	+\noindent\textbf{Abstract}
	61	+
	62	+\vspace{0.15cm}
	63	+
	64	+\noindent\WPabstract
	65	+
	66	+\vspace{0.4cm}
	67	+
	68	+\noindent\textbf{Keywords:} \WPkeywords
	69	+
	70	+\vspace{0.15cm}
	71	+
	72	+\noindent\textbf{JEL Classification:} \WPjel
	73	+
	74	+\vspace{0.3cm}
	75	+\noindent\rule{\textwidth}{0.4pt}
	76	+
	77	+\newpage

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added requirements.txt +8 −0

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	1	+numpy>=1.26
	2	+pandas>=2.0
	3	+duckdb>=0.10
	4	+scipy>=1.11
	5	+statsmodels>=0.14
	6	+networkx>=3.2
	7	+matplotlib>=3.8
	8	+seaborn>=0.13

added results/daily_rv_all.csv +6368 −0

		`@@ -0,0 +1,6368 @@`
	1	+date,ES,NQ,EURUSD,USDJPY,GBPUSD,GC,CL,BTC,ETH,VIX
	2	+2008-01-01,,,,,,,0.06800209477612582,,,
	3	+2008-01-02,0.18075905551144172,0.2268234851449807,,,,,0.26688596200556847,,,0.6172657662777021
	4	+2008-01-03,0.16214622449014918,0.20789909704334836,,,,,0.3010410698453539,,,0.42839724745095664
	5	+2008-01-04,0.24778964866649703,0.3049087968758,,,,,0.25915836262429065,,,1.0695958401628547
	6	+2008-01-06,0.050714260674747505,0.054332428531918234,,,,,0.07533477547322064,,,
	7	+2008-01-07,0.22967089658890766,0.37958555202115984,,,,,0.3098016292163067,,,0.7592847631114898
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	1919	+2014-01-04,,,,,,,,0.7760382709536381,,
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	1933	+2014-01-18,,,,,,,,0.6751192802590813,,
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	1968	+2014-02-22,,,,,,,,1.1947597428718337,,
	1969	+2014-02-23,0.04359092432736512,0.038847941257340445,0.015267218621204259,0.036318690209596396,0.02122750718904358,0.06278495632483796,0.04019594194118658,1.2658633400852675,,
	1970	+2014-02-24,0.10045005850450643,0.09739708376208218,0.04356446493805354,0.04884265720363246,0.06796563512719599,0.1331610483660445,0.1438539917974661,2.3425287706481392,,0.5737037636723412
	1971	+2014-02-25,0.1162133780161814,0.11598860025562556,0.04672966317203629,0.05811818533394469,0.0711149607705409,0.10539857382860693,0.14771806992412725,3.3031490978338796,,0.8681396449869542
	1972	+2014-02-26,0.10281983632265809,0.11518138981306321,0.048362704267095734,0.0523903210685205,0.05823712050591802,0.13016013716306823,0.12402112786162509,1.5690661133802093,,0.8547310787245495
	1973	+2014-02-27,0.11774600950520879,0.11883435045017093,0.05528186012242389,0.07756629490229482,0.056772843840095864,0.11190257464054618,0.157383440312099,0.8940106560230564,,0.6693608368795981
	1974	+2014-02-28,0.12000393884619619,0.1287335864522778,0.09247490879217908,0.06834580627021426,0.07431760607011566,0.11793016446645006,0.15143026004499627,1.2115162433871434,,0.8786443706353344
	1975	+2014-03-01,,,,,,,,0.8409114820079187,,
	1976	+2014-03-02,0.16596142005578965,0.15392811677348586,0.04479730912364255,0.04850629179403867,0.03050611244949671,0.12592333846979425,0.14537999550107933,0.8619597610398314,,
	1977	+2014-03-03,0.1410200909152306,0.16600681993321076,0.05793766715316826,0.055516890887506005,0.07480517440085209,0.11911542180522168,0.20259374993990711,2.3387860266012437,,0.890114228336012
	1978	+2014-03-04,0.14323918346868691,0.1427040126131042,0.05675022581618985,0.06436255944913102,0.054725034691856335,0.14910443430279346,0.17946794929874355,1.0854214768159716,,1.6932007453031195
	1979	+2014-03-05,0.08555711910048595,0.0839443434150274,0.059679315014269735,0.06499927087795208,0.05674466615373944,0.09861109028354932,0.16298348512796604,0.8789406571161363,,0.5949922837668624
	1980	+2014-03-06,0.07465599361847329,0.08446757957459056,0.06622132231852024,0.06194496088059363,0.05921565012477869,0.13334356655518867,0.21097106472893346,0.7383053239121096,,0.41873264650161707
	1981	+2014-03-07,0.12025160286867649,0.14207422106731077,0.05519375658491377,0.10914113535537158,0.05788097363830119,0.2145501444693939,0.15235382302027445,0.9690180739035957,,0.9792497895811643
	1982	+2014-03-08,,,,,,,,0.8229088125878646,,
	1983	+2014-03-09,0.03984114244184923,0.03891475823142298,0.013398698193268712,0.039105413360245256,0.022775146431384667,0.08799839164074769,0.04858355228247182,0.8609975595409729,,
	1984	+2014-03-10,0.09436799631136404,0.11288554063679664,0.04046837879205828,0.054761870678392464,0.05664994513779123,0.11163593420511357,0.16727314524057177,0.9009363626954809,,1.0662611062195522
	1985	+2014-03-11,0.10017905011220195,0.11522700610422801,0.04324655947384482,0.06625998173182107,0.047326719425209655,0.1467167496401464,0.1475585404348338,0.8923393730392379,,0.6484082451879943
	1986	+2014-03-12,0.11023231365400087,0.13901353522184517,0.04574497323114425,0.061214157423704445,0.056656505022007954,0.12525271373159705,0.2146906612607256,0.7035722978127432,,0.9333304533614202
	1987	+2014-03-13,0.13763043346991854,0.173847683486096,0.08192481579583204,0.09377596830106248,0.06577495661048852,0.1166839874881255,0.16205872263631213,0.5195199006658716,,1.0538887860050916
	1988	+2014-03-14,0.13497371824761167,0.1552780602810992,0.05592191165483384,0.07524442766044492,0.05732065773970159,0.13089088974816326,0.15657778467511085,0.5745486392016016,,1.1856565100235053
	1989	+2014-03-15,,,,,,,,0.42476521357591596,,
	1990	+2014-03-16,0.05146070866672445,0.05677018585442298,0.017708375269278674,0.041871635572975165,0.018703797026974542,0.10041263528666393,0.04627549084322475,0.37592307859209284,,
	1991	+2014-03-17,0.11598715022443608,0.1293860383767581,0.048441475235477455,0.06073253746732492,0.0419671455416963,0.14489649769333568,0.154327021648718,0.4057537537357509,,1.7264004171228533
	1992	+2014-03-18,0.11273343933587833,0.12780052456233423,0.06150099396324203,0.07682988595713733,0.058766089580792866,0.12506947161743034,0.13186882557919008,0.64950458049157,,0.75912582620016
	1993	+2014-03-19,0.13816799651344672,0.14180058446986943,0.07063567572434341,0.10056796926516437,0.08025242884259819,0.20585332984327795,0.14391450102584816,0.5377022033466021,,1.1525751799165882
	1994	+2014-03-20,0.11154051967933709,0.12137943758814594,0.05697716319159097,0.05194600119690027,0.04950787752160175,0.14133196190956127,0.16991251747372701,0.7062244726857133,,0.8186328409673151
	1995	+2014-03-21,0.11352455415829055,0.15294414360828795,0.05288722857657281,0.0593645054528486,0.047873266608160533,0.12559997175589852,0.16079806123193324,1.1512581182081525,,1.031308680284338
	1996	+2014-03-22,,,,,,,,0.7884808894699383,,
	1997	+2014-03-23,0.04330194429074817,0.038651461744834394,0.026257639454122614,0.041555705520170516,0.024183851657134978,0.07142001151127021,0.0521557449944113,0.5152764087241225,,
	1998	+2014-03-24,0.12562310557767653,0.18947973060543813,0.06473169895840611,0.05452305923540524,0.04761372482313284,0.14315741184506414,0.14170614105202253,0.742554057389397,,0.9410434364449871
	1999	+2014-03-25,0.10940857815652572,0.16490741251257693,0.06526538843145466,0.04735315821736256,0.0512304294432673,0.12178786709793472,0.18544943353503918,0.740391674185466,,1.3304162872679792
	2000	+2014-03-26,0.11385434465014999,0.1622276075049441,0.05857202380221318,0.06330783522468808,0.05882303179654702,0.12339865372983182,0.13948020001399022,0.6357031764000134,,1.0091827884328692
	2001	+2014-03-27,0.14087622740170072,0.22027143513890265,0.05999100652616926,0.06416083989689286,0.07587093274470205,0.14477035496058516,0.1279275183089978,2.0559040692329953,,1.0796822093355596
	2002	+2014-03-28,0.10655782558723577,0.14357296336460362,0.05840607422301913,0.054747600246964186,0.04393891163922603,0.13345033037967757,0.13496005881979584,1.3881046319192594,,0.8279966520738196
	2003	+2014-03-29,,,,,,,,0.7689552543486986,,
	2004	+2014-03-30,0.06151574773061111,0.0671775195941784,0.02087777557273412,0.02976891883099889,0.019613318040194647,0.04858838139754393,0.04026112970529346,1.410550184076363,,
	2005	+2014-03-31,0.0876149998791205,0.1310298960100879,0.06112259923935736,0.06808659976263724,0.05160457452391855,0.1306576803233913,0.14145887857789652,1.4971022093003605,,0.6995402719090927
	2006	+2014-04-01,0.07920243246672476,0.11513833365365282,0.042133517491733156,0.05529975322756471,0.04274386728890805,0.1104307782654373,0.16243817011831263,1.2954425563522156,,0.7190838606129235
	2007	+2014-04-02,0.083926957288233,0.12875204151372963,0.04351032490414376,0.05297384449971949,0.04888166663468048,0.11774252877392576,0.14896522012259814,1.6651912787541159,,0.569008998342391
	2008	+2014-04-03,0.08054227989994306,0.1260878250654759,0.0789899313400174,0.047040435552337445,0.04900876721400495,0.10704267406231888,0.12899093688486876,1.6146748076757884,,0.5620691268938544
	2009	+2014-04-04,0.12886892106307068,0.23776607196494984,0.06615202638265934,0.0641191397390057,0.0505591393964545,0.15108909637214074,0.11203891163315972,1.186238429614937,,1.3467971408833253
	2010	+2014-04-05,,,,,,,,0.8532761713432464,,
	2011	+2014-04-06,0.03970391653515435,0.05011627167473769,0.011990730933139501,0.02080811475680337,0.012286074191052314,0.036416136110025324,0.036908946263742776,0.8131867406803445,,
	2012	+2014-04-07,0.13533812213442165,0.23321954073954265,0.033297535483241686,0.06606134177612652,0.033637197595325324,0.08758751602680992,0.14174749674593942,0.7399233339300377,,1.3938377772583164
	2013	+2014-04-08,0.11919912145267748,0.16943493064363088,0.045851600244357804,0.08275616075338084,0.06507000049162044,0.11138797426431181,0.17100447948878922,0.7087204525729045,,0.9307789812744554
	2014	+2014-04-09,0.09536578926033411,0.137562117629992,0.06027825719938754,0.07723582594021293,0.052141548195089475,0.15276592649803616,0.1216702084150363,0.6684041557518272,,0.6615857302052733
	2015	+2014-04-10,0.1533446182595246,0.21013047519974623,0.038608413901279344,0.08564861571695276,0.04482054340827803,0.11229470878071966,0.12399476126992152,2.0746854680856512,,1.1489848812735675
	2016	+2014-04-11,0.1619471017271402,0.25201050679978365,0.03448937546705296,0.06281366620408227,0.04091422128987828,0.09442323858013768,0.12663366449004637,1.8681758673797426,,1.270174920389587
	2017	+2014-04-12,,,,,,,,1.1013149158312472,,
	2018	+2014-04-13,0.05711670668420815,0.06958322479537399,0.04025003073561133,0.030364086781504988,0.018939835151846315,0.07633564341699893,0.08477162916299799,0.9811573578730973,,
	2019	+2014-04-14,0.12533158621338944,0.15928290438499354,0.04276291122830043,0.05453777848436642,0.03887744531091859,0.10770436840744277,0.128106589912519,1.7331806618367074,,1.2164871331903975
	2020	+2014-04-15,0.1621831871903867,0.23585119792409293,0.045855189782140746,0.06126189002109178,0.07492297873919199,0.19266281235801375,0.12600831139414284,1.340838478375707,,1.130848870695549
	2021	+2014-04-16,0.11477952517740626,0.1885010384144489,0.04723197809353823,0.05264038118270105,0.05533420039480466,0.12426206393229501,0.14252055061729849,1.506010064331511,,1.2805771095308893
	2022	+2014-04-17,0.09399164344093854,0.16545105259267004,0.03665566555302586,0.042575324522368174,0.034318715174138766,0.10247233896036927,0.1489916355487225,1.1968930109748948,,0.7489692201953883
	2023	+2014-04-18,,,0.01582095673655051,0.01555472564293586,0.031964574850830124,,,0.8662148846509097,,
	2024	+2014-04-19,,,,,,,,1.0085503783134657,,
	2025	+2014-04-20,0.02881748497870197,0.032000941727765124,0.014762427297808531,0.02513307132463995,0.02014242275796837,0.14251563167058823,0.03807047293880043,0.9282522171969251,,
	2026	+2014-04-21,0.07192170808607447,0.1311467253105765,0.024905310341711673,0.029579124243483065,0.024811290380208136,0.12617098772220414,0.10521315119432116,0.9104433633289059,,1.1500410152361666
	2027	+2014-04-22,0.07157305828193489,0.09929364192777711,0.037688759131404376,0.03771237412589006,0.03605282659577755,0.10981330479144165,0.13438842838237938,0.7398984116192315,,0.46512335966874413
	2028	+2014-04-23,0.09841064463999045,0.19542878809170344,0.052196049561401225,0.056769437224192455,0.045558348076873506,0.09077483073544648,0.13860076825460624,0.5046929132730942,,0.4526875077975517
	2029	+2014-04-24,0.11002454240042579,0.18918522850672692,0.04665901269509077,0.059560767277804,0.04170084961887696,0.19865948307527964,0.13051779815450923,0.7688842744020015,,0.9614683089290007
	2030	+2014-04-25,0.09700609413409407,0.1408167761714522,0.02996394731469484,0.04021086197758086,0.030974378036621245,0.09655100908366375,0.13594711849651367,1.4171602824285594,,0.9511320850906589
	2031	+2014-04-26,,,,,,,,0.7217114356705473,,
	2032	+2014-04-27,0.026971386648854803,0.029510209341032604,0.018844575433900217,0.01894389397024959,0.018924217197477212,0.04547496507356096,0.0436467680204855,0.9313015353222865,,
	2033	+2014-04-28,0.1396013640564778,0.2207461696467225,0.04006619664947955,0.04555443915375347,0.03601827109688185,0.1082779322449587,0.13287885585265516,1.0254172074550658,,0.8988677611663866
	2034	+2014-04-29,0.08112470304420766,0.14279624238273875,0.04857860467806815,0.041787699580164386,0.04150239423509657,0.13412185559896672,0.14117143509839114,0.9300343607100209,,0.5375694084662743
	2035	+2014-04-30,0.10660697599682752,0.1459504208951723,0.05576497465025554,0.0663893078340718,0.049842472621147084,0.196896998303146,0.15400758564998943,0.7681833695543324,,0.7075573769630558
	2036	+2014-05-01,0.08310621142094188,0.12049298319338851,0.025962894018348878,0.03488352708939146,0.04021219059255305,0.1311321376090951,0.14715697371776404,0.7172930562647694,,0.6963637301438214
	2037	+2014-05-02,0.10850263650446348,0.15457460496213318,0.05619641061266816,0.0888652632382221,0.04711853958577814,0.16992982053602032,0.1270485517975919,0.6677165770325033,,0.6969661632361907
	2038	+2014-05-03,,,,,,,,0.785064550143394,,
	2039	+2014-05-04,0.031845926672164154,0.03350873181988787,0.016275169270112265,0.0284374846799717,0.014100944718068628,0.07462267949678704,0.03014574546069296,0.847312028079157,,
	2040	+2014-05-05,0.09107067786768332,0.1283036544522806,0.02570176185055529,0.03761612233202725,0.024505534918062327,0.09117577587120039,0.1345340303200613,0.7496194182914988,,1.4855122326144503
	2041	+2014-05-06,0.09477423621630947,0.12758510307885354,0.04333863041184615,0.05348985884354153,0.04644139979892006,0.10151090308400995,0.13755878982311837,0.6681260077324246,,0.5915698284111672
	2042	+2014-05-07,0.1458304690270489,0.20899042182900743,0.03919446074157452,0.07032506886713076,0.03389134872449479,0.1336375722530996,0.14185054446777712,0.8680675432951824,,1.0318319572907415
	2043	+2014-05-08,0.10905105352409536,0.17136117207142998,0.09775788787568117,0.05699723246153834,0.04646145367709606,0.10907138767798502,0.1290419149144848,0.5892712637063564,,0.6779237921702698
	2044	+2014-05-09,0.10565336204723393,0.16609001613490965,0.045187831936120214,0.03528599655363367,0.04524459221136511,0.08452043988750876,0.1413560632391963,0.5708843739435575,,0.7116611840673887
	2045	+2014-05-10,,,,,,,,0.5563611216176066,,
	2046	+2014-05-11,0.027008218963431533,0.029881599040165126,0.01319607416401142,0.027990665839014862,0.02428708227015665,0.0856032801973976,0.03624775183079136,0.7313384549078307,,
	2047	+2014-05-12,0.06712412263360007,0.09907654940531968,0.032269199856945235,0.036077641438501666,0.033009762169813196,0.11471852798659293,0.11807419927467483,0.5394575811497536,,0.6829094896513767
	2048	+2014-05-13,0.06951878672348,0.11022375054841242,0.056149085680455985,0.04467300034945885,0.0401633502952783,0.10978843972394922,0.13911954812401997,0.41417569909427604,,0.7896907681272063
	2049	+2014-05-14,0.07818207890922874,0.11303907071186138,0.04200677807842627,0.051493784345327864,0.06109503978137508,0.10524827373991491,0.10832854957323793,0.5198859965734833,,0.5696077833962897
	2050	+2014-05-15,0.1164875560521808,0.16514835937786815,0.05848060196249486,0.06986261196475314,0.04581506124755459,0.1493694749205793,0.10477278723951404,0.41012413256091124,,1.1922072455119899
	2051	+2014-05-16,0.09621453976383387,0.13211800323435777,0.04252931242749946,0.05169494598704329,0.03445852280638997,0.09629782024887643,0.08955468815115511,0.4045258147899243,,0.783445712625854
	2052	+2014-05-17,,,,,,,,0.279273465027839,,
	2053	+2014-05-18,0.026146704161210406,0.029913279726312934,0.01150154415237467,0.02411657982943118,0.015302361962056121,0.04323997075494478,0.030328565739322876,0.19439531650591094,,
	2054	+2014-05-19,0.08117348143218349,0.10728195539576776,0.03355879571481762,0.053117281015597456,0.03349305128735921,0.1007222149765752,0.09028068749609808,0.4763050296139635,,0.8733218363011779
	2055	+2014-05-20,0.09768944372508095,0.1329835280533031,0.03517600594885697,0.05099570847924151,0.04415107587803266,0.11325349033177405,0.11556260943217625,0.9397343015760522,,0.7998485014871403
	2056	+2014-05-21,0.081910901933511,0.10707407792867377,0.049916517615492095,0.07083505873871243,0.05454038155087132,0.11358593459667159,0.1160054276437247,0.4686831071919716,,1.262494684287537
	2057	+2014-05-22,0.06774225640505967,0.0865096327207184,0.04137956571126027,0.04831256809703671,0.04917736887028136,0.0865568754165851,0.0910744144986853,0.8499050633410489,,0.5599634642638452
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	2059	+2014-05-24,,,,,,,,0.5464108367429087,,
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added results/rolling_total_spillover.csv +3452 −0

		`@@ -0,0 +1,3452 @@`
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	3376	+2025-12-24,68.51931821665553
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	3378	+2025-12-26,67.85809853220945
	3379	+2025-12-27,67.89530074752044
	3380	+2025-12-28,68.17722506096332
	3381	+2025-12-29,68.33761112381033
	3382	+2025-12-30,68.60740510114226
	3383	+2025-12-31,68.80253490755567
	3384	+2026-01-01,68.95188794917608
	3385	+2026-01-02,69.11772689552403
	3386	+2026-01-03,69.38345721304674
	3387	+2026-01-04,69.52948172897659
	3388	+2026-01-05,69.74898808712378
	3389	+2026-01-06,70.03541174501787
	3390	+2026-01-07,70.02355208131232
	3391	+2026-01-08,70.08569999292565
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	3395	+2026-01-12,69.97523951456891
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	3398	+2026-01-15,69.21046643755606
	3399	+2026-01-16,69.31641642951247
	3400	+2026-01-17,69.49667602439206
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	3402	+2026-01-19,69.17013539922212
	3403	+2026-01-20,69.35658178797458
	3404	+2026-01-21,69.50334409636686
	3405	+2026-01-22,69.57187081926628
	3406	+2026-01-23,69.37677495779023
	3407	+2026-01-24,69.16346745806716
	3408	+2026-01-25,69.06694005372906
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	3411	+2026-01-28,69.02657018940673
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	3413	+2026-01-30,71.33884205120185
	3414	+2026-01-31,71.29562640405935
	3415	+2026-02-01,71.47478589811794
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	3417	+2026-02-03,71.38479679704007
	3418	+2026-02-04,71.30496691783745
	3419	+2026-02-05,72.29375947853408
	3420	+2026-02-06,71.85281529233592
	3421	+2026-02-07,71.95751795615062
	3422	+2026-02-08,71.56746939482446
	3423	+2026-02-09,71.56400517185577
	3424	+2026-02-10,71.54054636446854
	3425	+2026-02-11,71.85550736636708
	3426	+2026-02-12,71.87615906733207
	3427	+2026-02-13,70.85774625621842
	3428	+2026-02-14,70.46108827101943
	3429	+2026-02-15,70.28830515361706
	3430	+2026-02-16,70.36447123001975
	3431	+2026-02-17,70.43204041473402
	3432	+2026-02-18,70.27675668777145
	3433	+2026-02-19,70.11566591779275
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	3435	+2026-02-21,70.45557008654897
	3436	+2026-02-22,70.04935282921933
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	3438	+2026-02-24,70.2018841158014
	3439	+2026-02-25,70.1443648168611
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	3443	+2026-03-01,69.90500807699082
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	3447	+2026-03-05,71.20127911661297
	3448	+2026-03-06,71.16183313808031
	3449	+2026-03-07,70.97448699508966
	3450	+2026-03-08,71.32204925019656
	3451	+2026-03-09,73.07014366265825
	3452	+2026-03-10,70.6063631568688

added results/table1_descriptive_stats.csv +11 −0

		`@@ -0,0 +1,11 @@`
	1	+Asset,Class,N_obs,Date_Start,Date_End,Mean,Std,Skewness,Kurtosis,Min,Max
	2	+ES,Equity,1283243,2008-01-02,2026-03-11,0.000001,0.000733,-0.053484,35.335927,-0.014999,0.015002
	3	+NQ,Equity,1275095,2008-01-02,2026-03-11,0.000002,0.000841,-0.025103,30.113193,-0.016984,0.017033
	4	+EURUSD,FX,1205222,2010-01-03,2026-03-11,-0.000000,0.000318,0.117616,20.379603,-0.006278,0.006377
	5	+USDJPY,FX,1204270,2010-01-03,2026-03-11,0.000001,0.000337,-0.116010,27.671317,-0.006996,0.006995
	6	+GBPUSD,FX,1204351,2010-01-03,2026-03-11,-0.000000,0.000333,0.093232,21.825239,-0.006874,0.006873
	7	+GC,Commodity,1289111,2008-01-27,2026-03-11,0.000001,0.000671,-0.199546,25.346678,-0.013582,0.013588
	8	+CL,Commodity,1292389,2008-01-01,2026-03-11,-0.000002,0.001495,-0.144604,38.206510,-0.032803,0.033536
	9	+BTC,Crypto,1319754,2013-04-01,2026-03-11,0.000006,0.006484,0.023574,55.520004,-0.148996,0.148396
	10	+ETH,Crypto,1014094,2016-03-11,2026-03-11,0.000005,0.005972,0.025174,62.965033,-0.126621,0.127282
	11	+VIX,Volatility,550857,2008-01-02,2026-03-11,-0.000013,0.006880,0.997232,52.564569,-0.145845,0.146462

added results/table2_connectedness_full.csv +13 −0

		`@@ -0,0 +1,13 @@`
	1	+,ES,NQ,EURUSD,USDJPY,GBPUSD,GC,CL,BTC,ETH,VIX,FROM
	2	+ES,28.60,25.46,8.42,6.56,7.15,9.11,8.42,0.22,0.18,5.88,71.40
	3	+NQ,26.73,27.56,8.72,6.50,7.44,9.01,8.13,0.20,0.16,5.54,72.44
	4	+EURUSD,11.44,11.22,25.73,14.26,17.36,10.96,8.05,0.04,0.22,0.73,74.27
	5	+USDJPY,8.91,8.71,15.73,38.55,11.58,9.14,5.59,0.07,0.27,1.46,61.45
	6	+GBPUSD,11.11,10.64,18.70,11.69,29.57,9.76,7.66,0.08,0.24,0.55,70.43
	7	+GC,11.82,11.38,12.66,9.50,9.55,34.49,8.04,0.19,0.23,2.14,65.51
	8	+CL,12.89,11.23,7.90,4.99,7.08,9.32,45.26,0.04,0.08,1.21,54.74
	9	+BTC,0.09,0.09,0.09,0.18,0.08,0.33,0.08,79.33,19.33,0.40,20.67
	10	+ETH,0.17,0.27,0.23,0.28,0.14,0.15,0.16,20.61,77.88,0.11,22.12
	11	+VIX,15.03,13.15,2.24,2.48,1.39,4.83,1.42,0.45,0.39,58.62,41.38
	12	+TO,98.20,92.15,74.69,56.42,61.77,62.61,47.56,21.90,21.10,18.01,55.44
	13	+NET,26.80,19.72,0.42,-5.03,-8.66,-2.91,-7.18,1.23,-1.03,-23.37,

added results/table3a_connectedness_precovid.csv +13 −0

		`@@ -0,0 +1,13 @@`
	1	+,ES,NQ,EURUSD,USDJPY,GBPUSD,GC,CL,BTC,ETH,VIX,FROM
	2	+ES,31.28,28.97,4.13,9.40,1.56,8.50,6.49,0.04,0.73,8.91,68.72
	3	+NQ,30.50,29.20,4.22,9.76,1.73,8.47,6.82,0.05,0.68,8.57,70.80
	4	+EURUSD,12.81,13.10,24.07,12.86,13.55,12.28,9.47,0.20,0.25,1.41,75.93
	5	+USDJPY,21.57,20.77,7.13,20.47,3.18,11.91,7.45,0.05,0.32,7.15,79.53
	6	+GBPUSD,8.58,8.36,18.03,7.75,37.55,8.78,7.82,0.36,0.75,2.01,62.45
	7	+GC,15.92,16.16,9.08,14.70,4.57,25.03,9.37,0.65,0.21,4.31,74.97
	8	+CL,17.11,17.92,7.44,12.86,5.07,11.03,25.67,0.19,0.16,2.54,74.33
	9	+BTC,7.05,5.55,0.22,1.40,0.29,2.22,1.71,72.98,6.82,1.75,27.02
	10	+ETH,6.71,6.03,0.56,1.41,0.39,1.74,2.40,24.57,55.18,1.02,44.82
	11	+VIX,24.91,22.85,1.82,7.96,0.31,5.47,3.25,0.88,1.15,31.40,68.60
	12	+TO,145.15,139.71,52.64,78.09,30.65,70.40,54.77,27.00,11.08,37.68,64.72
	13	+NET,76.43,68.91,-23.29,-1.44,-31.79,-4.57,-19.56,-0.02,-33.74,-30.93,

added results/table3b_connectedness_covid.csv +13 −0

		`@@ -0,0 +1,13 @@`
	1	+,ES,NQ,EURUSD,USDJPY,GBPUSD,GC,CL,BTC,ETH,VIX,FROM
	2	+ES,20.14,20.57,10.92,16.17,9.55,7.15,5.58,4.44,2.42,3.06,79.86
	3	+NQ,19.44,21.13,10.82,16.71,9.35,7.32,5.77,3.90,2.24,3.33,78.87
	4	+EURUSD,8.45,9.70,21.78,19.90,17.77,10.22,7.55,0.96,1.54,2.14,78.22
	5	+USDJPY,5.62,7.91,14.35,33.56,11.12,7.25,3.88,5.40,2.96,7.95,66.44
	6	+GBPUSD,11.05,11.32,17.02,18.62,23.93,7.94,5.37,2.11,2.04,0.61,76.07
	7	+GC,8.08,9.56,13.04,14.40,9.18,23.56,12.39,3.87,4.33,1.58,76.44
	8	+CL,4.62,5.18,8.68,4.54,6.46,17.24,48.99,1.49,2.23,0.58,51.01
	9	+BTC,2.56,2.75,5.86,16.17,2.21,6.29,6.52,34.81,15.95,6.88,65.19
	10	+ETH,3.36,3.15,3.97,8.21,1.05,3.11,4.43,17.33,51.56,3.83,48.44
	11	+VIX,5.53,7.15,7.57,12.00,5.64,0.69,0.65,4.34,2.46,53.96,46.04
	12	+TO,68.70,77.30,92.22,126.73,72.32,67.22,52.13,43.85,36.16,29.96,66.66
	13	+NET,-11.16,-1.57,13.99,60.29,-3.75,-9.22,1.12,-21.34,-12.28,-16.07,

added results/table3c_connectedness_ratehikes.csv +13 −0

		`@@ -0,0 +1,13 @@`
	1	+,ES,NQ,EURUSD,USDJPY,GBPUSD,GC,CL,BTC,ETH,VIX,FROM
	2	+ES,21.93,19.46,11.67,3.83,10.00,12.19,9.43,3.86,3.36,4.28,78.07
	3	+NQ,20.68,21.65,11.51,3.64,9.39,11.83,9.89,4.15,3.56,3.70,78.35
	4	+EURUSD,11.43,11.18,22.88,8.62,17.01,13.51,10.43,2.47,1.76,0.71,77.12
	5	+USDJPY,6.17,5.84,13.29,38.89,11.28,10.30,6.04,3.01,2.63,2.55,61.11
	6	+GBPUSD,9.39,8.55,18.53,8.69,31.36,12.00,7.51,1.88,1.60,0.48,68.64
	7	+GC,12.94,11.99,14.17,6.70,11.14,22.06,11.48,3.86,3.75,1.91,77.94
	8	+CL,11.58,11.63,12.04,4.99,8.82,13.66,30.14,2.93,2.43,1.78,69.86
	9	+BTC,3.45,2.92,1.36,1.30,0.73,2.32,1.24,43.43,38.56,4.68,56.57
	10	+ETH,3.53,3.05,1.30,1.19,0.79,2.70,1.51,38.24,43.91,3.79,56.09
	11	+VIX,5.14,3.94,2.76,4.92,2.30,3.23,2.16,4.08,3.89,67.59,32.41
	12	+TO,84.31,78.57,86.62,43.88,71.46,81.74,59.68,64.47,61.54,23.88,65.62
	13	+NET,6.24,0.22,9.50,-17.23,2.82,3.80,-10.18,7.90,5.45,-8.53,

added results/table4_session_granger.csv +28 −0

		`@@ -0,0 +1,28 @@`
	1	+Session,Cause,Effect,F_stat,p_value,Significant
	2	+Asian,VIX,ES,4.3033,0.0018,Yes
	3	+Asian,VIX,NQ,4.1807,0.0022,Yes
	4	+Asian,VIX,BTC,1.6421,0.1608,No
	5	+Asian,ES,NQ,4.4485,0.0014,Yes
	6	+Asian,ES,BTC,0.5810,0.6764,No
	7	+Asian,NQ,BTC,0.4408,0.7792,No
	8	+Asian,ES,VIX,19.8639,0.0000,Yes
	9	+Asian,NQ,VIX,16.7083,0.0000,Yes
	10	+Asian,BTC,VIX,1.7960,0.1268,No
	11	+European,VIX,ES,4.3033,0.0018,Yes
	12	+European,VIX,NQ,4.1807,0.0022,Yes
	13	+European,VIX,BTC,1.6421,0.1608,No
	14	+European,ES,NQ,4.4485,0.0014,Yes
	15	+European,ES,BTC,0.5810,0.6764,No
	16	+European,NQ,BTC,0.4408,0.7792,No
	17	+European,ES,VIX,19.8639,0.0000,Yes
	18	+European,NQ,VIX,16.7083,0.0000,Yes
	19	+European,BTC,VIX,1.7960,0.1268,No
	20	+US,VIX,ES,4.3033,0.0018,Yes
	21	+US,VIX,NQ,4.1807,0.0022,Yes
	22	+US,VIX,BTC,1.6421,0.1608,No
	23	+US,ES,NQ,4.4485,0.0014,Yes
	24	+US,ES,BTC,0.5810,0.6764,No
	25	+US,NQ,BTC,0.4408,0.7792,No
	26	+US,ES,VIX,19.8639,0.0000,Yes
	27	+US,NQ,VIX,16.7083,0.0000,Yes
	28	+US,BTC,VIX,1.7960,0.1268,No

added scripts/01_analysis.py +814 −0

		`@@ -0,0 +1,814 @@`
	1	+"""
	2	+Intraday Volatility Transmission Across Asset Classes
	3	+Diebold-Yilmaz Connectedness Analysis
	4	+"""
	5	+
	6	+import os
	7	+import warnings
	8	+import numpy as np
	9	+import pandas as pd
	10	+import matplotlib
	11	+matplotlib.use('Agg')
	12	+import matplotlib.pyplot as plt
	13	+import matplotlib.patches as mpatches
	14	+import matplotlib.gridspec as gridspec
	15	+import seaborn as sns
	16	+import duckdb
	17	+from scipy import stats
	18	+import networkx as nx
	19	+from statsmodels.tsa.api import VAR
	20	+from statsmodels.tsa.stattools import grangercausalitytests
	21	+import traceback
	22	+
	23	+warnings.filterwarnings('ignore')
	24	+
	25	+# ─── Paths ────────────────────────────────────────────────────────────────────
	26	+ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
	27	+DATA_DIR = os.environ.get('WP6_DATA_DIR', os.path.join(ROOT, 'data', 'raw')) # *_5min.duckdb files (see data/raw/README.md)
	28	+RESULTS = os.path.join(ROOT, 'results')
	29	+FIGURES = os.path.join(ROOT, 'figures')
	30	+os.makedirs(FIGURES, exist_ok=True)
	31	+os.makedirs(RESULTS, exist_ok=True)
	32	+
	33	+plt.rcParams.update({
	34	+ 'font.size': 10, 'axes.titlesize': 11, 'axes.labelsize': 10,
	35	+ 'xtick.labelsize': 9, 'ytick.labelsize': 9, 'legend.fontsize': 9,
	36	+ 'figure.dpi': 150, 'savefig.dpi': 150, 'font.family': 'DejaVu Sans',
	37	+ 'axes.spines.top': False, 'axes.spines.right': False,
	38	+})
	39	+
	40	+ASSET_COLORS = {
	41	+ 'ES': '#1f77b4', 'NQ': '#aec7e8',
	42	+ 'EURUSD': '#2ca02c', 'USDJPY': '#98df8a', 'GBPUSD': '#d62728',
	43	+ 'GC': '#ff7f0e', 'CL': '#ffbb78',
	44	+ 'BTC': '#9467bd', 'ETH': '#c5b0d5',
	45	+ 'VIX': '#8c564b',
	46	+}
	47	+ASSET_CLASS = {
	48	+ 'ES': 'Equity', 'NQ': 'Equity',
	49	+ 'EURUSD': 'FX', 'USDJPY': 'FX', 'GBPUSD': 'FX',
	50	+ 'GC': 'Commodity', 'CL': 'Commodity',
	51	+ 'BTC': 'Crypto', 'ETH': 'Crypto',
	52	+ 'VIX': 'Volatility',
	53	+}
	54	+CLASS_COLOR = {
	55	+ 'Equity': '#1f77b4', 'FX': '#2ca02c',
	56	+ 'Commodity': '#ff7f0e', 'Crypto': '#9467bd', 'Volatility': '#8c564b',
	57	+}
	58	+
	59	+ASSETS = ['ES', 'NQ', 'EURUSD', 'USDJPY', 'GBPUSD', 'GC', 'CL', 'BTC', 'ETH', 'VIX']
	60	+
	61	+# ─── 1. Load 5-min data ───────────────────────────────────────────────────────
	62	+print("=" * 70)
	63	+print("Loading 5-min OHLCV data...")
	64	+
	65	+def load_asset(db_name, symbol):
	66	+ db_path = os.path.join(DATA_DIR, db_name)
	67	+ conn = duckdb.connect(db_path, read_only=True)
	68	+ df = conn.execute(
	69	+ f"SELECT datetime, close FROM ohlcv WHERE symbol='{symbol}' ORDER BY datetime"
	70	+ ).fetchdf()
	71	+ conn.close()
	72	+ df['datetime'] = pd.to_datetime(df['datetime'])
	73	+ df = df.set_index('datetime')
	74	+ df.columns = [symbol]
	75	+ return df
	76	+
	77	+futures_assets = {
	78	+ 'ES': 'futures_5min.duckdb',
	79	+ 'NQ': 'futures_5min.duckdb',
	80	+ 'GC': 'futures_5min.duckdb',
	81	+ 'CL': 'futures_5min.duckdb',
	82	+ 'VX': 'futures_5min.duckdb',
	83	+}
	84	+fx_assets = {
	85	+ 'EURUSD': 'fx_5min.duckdb',
	86	+ 'USDJPY': 'fx_5min.duckdb',
	87	+ 'GBPUSD': 'fx_5min.duckdb',
	88	+}
	89	+crypto_assets = {
	90	+ 'BTC': 'crypto_5min.duckdb',
	91	+ 'ETH': 'crypto_5min.duckdb',
	92	+}
	93	+index_assets = {
	94	+ 'VIX': 'index_5min.duckdb',
	95	+}
	96	+
	97	+raw_data = {}
	98	+for sym, db in {futures_assets, fx_assets, crypto_assets, index_assets}.items():
	99	+ print(f" Loading {sym} from {db}...")
	100	+ raw_data[sym] = load_asset(db, sym)
	101	+
	102	+print("Data loaded.\n")
	103	+
	104	+# ─── Compute 5-min log returns ────────────────────────────────────────────────
	105	+print("Computing 5-min log returns...")
	106	+log_returns = {}
	107	+for sym, df in raw_data.items():
	108	+ lr = np.log(df[sym] / df[sym].shift(1)).dropna()
	109	+ # Remove extreme outliers (> 20 std)
	110	+ mu, sigma = lr.mean(), lr.std()
	111	+ lr = lr[(lr - mu).abs() < 20 * sigma]
	112	+ log_returns[sym] = lr
	113	+
	114	+# ─── 1. Descriptive Statistics ────────────────────────────────────────────────
	115	+print("Computing descriptive statistics...")
	116	+desc_rows = []
	117	+for sym in ASSET_CLASS.keys():
	118	+ if sym not in log_returns:
	119	+ # VX → treat VX as proxy for VIX
	120	+ continue
	121	+ lr = log_returns[sym]
	122	+ row = {
	123	+ 'Asset': sym,
	124	+ 'Class': ASSET_CLASS.get(sym, 'Other'),
	125	+ 'N_obs': len(lr),
	126	+ 'Date_Start': lr.index.min().strftime('%Y-%m-%d'),
	127	+ 'Date_End': lr.index.max().strftime('%Y-%m-%d'),
	128	+ 'Mean': lr.mean(),
	129	+ 'Std': lr.std(),
	130	+ 'Skewness': stats.skew(lr),
	131	+ 'Kurtosis': stats.kurtosis(lr),
	132	+ 'Min': lr.min(),
	133	+ 'Max': lr.max(),
	134	+ }
	135	+ desc_rows.append(row)
	136	+
	137	+desc_df = pd.DataFrame(desc_rows)
	138	+desc_df.to_csv(os.path.join(RESULTS, 'table1_descriptive_stats.csv'), index=False, float_format='%.6f')
	139	+print(" Saved table1_descriptive_stats.csv")
	140	+print(desc_df[['Asset', 'N_obs', 'Mean', 'Std', 'Skewness', 'Kurtosis']].to_string(index=False))
	141	+
	142	+# ─── 2. Realized Volatility ───────────────────────────────────────────────────
	143	+print("\nComputing daily realized volatility...")
	144	+
	145	+def compute_rv(log_ret_series, min_obs=20):
	146	+ """Annualized daily realized volatility."""
	147	+ df = log_ret_series.to_frame(name='ret')
	148	+ df['date'] = df.index.date
	149	+ grouped = df.groupby('date')['ret']
	150	+ rv = grouped.apply(lambda x: np.sqrt(np.sum(x*2)) np.sqrt(252) if len(x) >= min_obs else np.nan)
	151	+ rv.index = pd.to_datetime(rv.index)
	152	+ return rv.dropna()
	153	+
	154	+rv_dict = {}
	155	+for sym in ASSET_CLASS.keys():
	156	+ if sym not in log_returns:
	157	+ continue
	158	+ rv_dict[sym] = compute_rv(log_returns[sym])
	159	+ print(f" {sym}: {len(rv_dict[sym])} trading days, RV mean = {rv_dict[sym].mean():.4f}")
	160	+
	161	+# Combine into DataFrame
	162	+rv_df = pd.DataFrame(rv_dict)
	163	+rv_df.index.name = 'date'
	164	+rv_df.to_csv(os.path.join(RESULTS, 'daily_rv_all.csv'))
	165	+print(" Saved daily_rv_all.csv")
	166	+
	167	+# ─── Fig 1: RV Time Series ────────────────────────────────────────────────────
	168	+print("\nPlotting Fig 1: RV Time Series...")
	169	+fig, axes = plt.subplots(5, 2, figsize=(14, 16), sharex=False)
	170	+axes = axes.flatten()
	171	+
	172	+asset_order = ['ES', 'NQ', 'EURUSD', 'USDJPY', 'GBPUSD', 'GC', 'CL', 'BTC', 'ETH', 'VIX']
	173	+for i, sym in enumerate(asset_order):
	174	+ if sym not in rv_dict:
	175	+ continue
	176	+ ax = axes[i]
	177	+ rv_s = rv_dict[sym]
	178	+ color = ASSET_COLORS.get(sym, 'steelblue')
	179	+ ax.plot(rv_s.index, rv_s.values, color=color, linewidth=0.7, alpha=0.9)
	180	+ ax.fill_between(rv_s.index, rv_s.values, alpha=0.15, color=color)
	181	+ ax.set_title(f'{sym} ({ASSET_CLASS.get(sym, "")})')
	182	+ ax.set_ylabel('Annualized RV')
	183	+ ax.xaxis.set_major_locator(matplotlib.dates.YearLocator(2))
	184	+ ax.xaxis.set_major_formatter(matplotlib.dates.DateFormatter('%Y'))
	185	+ plt.setp(ax.xaxis.get_majorticklabels(), rotation=45, ha='right')
	186	+
	187	+plt.suptitle('Daily Realized Volatility — All Assets (5-min, Annualized)', fontsize=13, y=1.01)
	188	+plt.tight_layout()
	189	+fig.savefig(os.path.join(FIGURES, 'fig1_rv_timeseries.png'), dpi=150, bbox_inches='tight')
	190	+plt.close()
	191	+print(" Saved fig1_rv_timeseries.png")
	192	+
	193	+# ─── Helper: Diebold-Yilmaz GFEVD ────────────────────────────────────────────
	194	+def compute_gfevd(var_result, H=10):
	195	+ """
	196	+ Generalized Forecast Error Variance Decomposition (Pesaran-Shin).
	197	+ Returns an (n x n) matrix where entry [i,j] = share of forecast error
	198	+ variance of variable i attributable to shocks from variable j.
	199	+ """
	200	+ n = var_result.k_ar # actually number of variables
	201	+ coefs = var_result.coefs # shape (p, n, n)
	202	+ sigma = var_result.sigma_u # (n, n) residual covariance
	203	+ n = sigma.shape[0]
	204	+ p = coefs.shape[0]
	205	+
	206	+ # Build MA coefficient matrices Psi_h via recursive computation
	207	+ # Psi_0 = I, Psi_h = sum_{j=1..min(h,p)} A_j @ Psi_{h-j}
	208	+ psi = [np.eye(n)]
	209	+ for h in range(1, H + 1):
	210	+ psi_h = np.zeros((n, n))
	211	+ for j in range(1, min(h, p) + 1):
	212	+ psi_h += coefs[j-1] @ psi[h-j]
	213	+ psi.append(psi_h)
	214	+
	215	+ # GFEVD: theta[i,j] = (1/sigma[j,j]) * sum_{h=0}^{H-1} (e_i' Psi_h Sigma e_j)^2
	216	+ # / sum_{h=0}^{H-1} (e_i' Psi_h Sigma Psi_h' e_i)
	217	+ sigma_diag = np.diag(sigma)
	218	+ gfevd = np.zeros((n, n))
	219	+
	220	+ for i in range(n):
	221	+ ei = np.zeros(n); ei[i] = 1.0
	222	+ denom = 0.0
	223	+ for h in range(H):
	224	+ denom += ei @ psi[h] @ sigma @ psi[h].T @ ei
	225	+ for j in range(n):
	226	+ ej = np.zeros(n); ej[j] = 1.0
	227	+ num = 0.0
	228	+ for h in range(H):
	229	+ num += (ei @ psi[h] @ sigma @ ej) ** 2
	230	+ gfevd[i, j] = num / (sigma_diag[j] * denom)
	231	+
	232	+ # Row-normalize so rows sum to 1
	233	+ row_sums = gfevd.sum(axis=1, keepdims=True)
	234	+ row_sums[row_sums == 0] = 1.0
	235	+ gfevd = gfevd / row_sums
	236	+ return gfevd
	237	+
	238	+
	239	+def compute_connectedness(rv_panel, assets, lag=4, H=10):
	240	+ """
	241	+ Given a DataFrame of RV series (rows=dates, cols=assets),
	242	+ fit VAR(lag), compute GFEVD at horizon H, return connectedness table.
	243	+ """
	244	+ # Use only complete rows
	245	+ data = rv_panel[assets].dropna()
	246	+ if len(data) < lag + H + 10:
	247	+ return None, None
	248	+
	249	+ model = VAR(data)
	250	+ try:
	251	+ res = model.fit(lag, trend='c')
	252	+ except Exception as e:
	253	+ print(f" VAR fit failed: {e}")
	254	+ return None, None
	255	+
	256	+ gfevd = compute_gfevd(res, H=H)
	257	+ n = len(assets)
	258	+
	259	+ # Build full connectedness table
	260	+ # Rows = "TO" (recipient of shocks), Cols = "FROM" (origin of shocks)
	261	+ # But DY convention: entry [i,j] = contribution of j to i's forecast error
	262	+ # TO_j = sum_{i != j} theta[i,j] / N * 100 (what j contributes to others)
	263	+ # FROM_i = sum_{j != i} theta[i,j] / N * 100 (what i receives from others)
	264	+
	265	+ # gfevd[i,j] = share of i's FEVD from j's shock
	266	+ # So: FROM_i = sum_{j!=i} gfevd[i,j] * 100
	267	+ # TO_j = sum_{i!=j} gfevd[i,j] * 100
	268	+
	269	+ # Total spillover index
	270	+ off_diag = gfevd.copy()
	271	+ np.fill_diagonal(off_diag, 0.0)
	272	+ TSI = off_diag.sum() / n * 100
	273	+
	274	+ # Directional
	275	+ FROM = off_diag.sum(axis=1) * 100 # what each asset receives
	276	+ TO = off_diag.sum(axis=0) * 100 # what each asset transmits
	277	+ NET = TO - FROM
	278	+
	279	+ # Build output DataFrame (DY table format)
	280	+ # gfevd * 100 → percentages
	281	+ tbl = pd.DataFrame(gfevd * 100, index=assets, columns=assets)
	282	+ tbl['FROM'] = FROM
	283	+ to_row = pd.Series(TO, index=assets)
	284	+ net_row = pd.Series(NET, index=assets)
	285	+ tbl.loc['TO'] = to_row
	286	+ tbl.loc['NET'] = net_row
	287	+ tbl.loc['TO', 'FROM'] = TSI
	288	+ tbl.loc['NET', 'FROM'] = np.nan
	289	+
	290	+ return tbl, TSI
	291	+
	292	+
	293	+# ─── 3. Full-Sample Connectedness ─────────────────────────────────────────────
	294	+print("\n" + "="*70)
	295	+print("Section 3: Full-Sample Connectedness (VAR-4, H=10)...")
	296	+
	297	+# Use VIX from index (not VX futures) as VIX is more common
	298	+# Find common sample: align all RV series
	299	+common_assets = [a for a in ASSET_CLASS.keys() if a in rv_dict]
	300	+rv_panel = pd.DataFrame({a: rv_dict[a] for a in common_assets})
	301	+
	302	+# Forward fill up to 5 days to handle weekends/holidays
	303	+rv_panel = rv_panel.ffill(limit=5)
	304	+
	305	+# Drop rows where more than 3 assets are missing
	306	+rv_panel = rv_panel.dropna(thresh=len(common_assets) - 2)
	307	+rv_panel = rv_panel.dropna()
	308	+
	309	+print(f" Common sample: {rv_panel.index[0].date()} to {rv_panel.index[-1].date()}, {len(rv_panel)} days")
	310	+print(f" Assets: {common_assets}")
	311	+
	312	+conn_table, tsi_full = compute_connectedness(rv_panel, common_assets, lag=4, H=10)
	313	+if conn_table is not None:
	314	+ conn_table.to_csv(os.path.join(RESULTS, 'table2_connectedness_full.csv'), float_format='%.2f')
	315	+ print(f" Total Spillover Index (full sample): {tsi_full:.2f}%")
	316	+ print(" NET spillovers:")
	317	+ for a in common_assets:
	318	+ print(f" {a:10s}: NET = {conn_table.loc['NET', a]:+.2f}%")
	319	+ print(" Saved table2_connectedness_full.csv")
	320	+else:
	321	+ print(" WARNING: Full-sample connectedness failed.")
	322	+
	323	+# ─── Fig 2: Connectedness Heatmap ─────────────────────────────────────────────
	324	+if conn_table is not None:
	325	+ print("\nPlotting Fig 2: Connectedness Heatmap...")
	326	+ heat_data = conn_table.loc[common_assets, common_assets].values.astype(float)
	327	+ fig, ax = plt.subplots(figsize=(11, 8))
	328	+ mask_diag = np.eye(len(common_assets), dtype=bool)
	329	+ im = ax.imshow(heat_data, cmap='RdYlBu_r', aspect='auto', vmin=0, vmax=heat_data.max())
	330	+ for i in range(len(common_assets)):
	331	+ for j in range(len(common_assets)):
	332	+ txt = f"{heat_data[i,j]:.1f}"
	333	+ color = 'white' if heat_data[i,j] > heat_data.max() * 0.6 else 'black'
	334	+ ax.text(j, i, txt, ha='center', va='center', fontsize=8, color=color, fontweight='bold')
	335	+ ax.set_xticks(range(len(common_assets)))
	336	+ ax.set_yticks(range(len(common_assets)))
	337	+ ax.set_xticklabels(common_assets, rotation=45, ha='right')
	338	+ ax.set_yticklabels(common_assets)
	339	+ ax.set_xlabel('FROM (shock origin)')
	340	+ ax.set_ylabel('TO (shock recipient)')
	341	+ ax.set_title(f'Diebold-Yilmaz Connectedness Matrix (Full Sample)\nTotal Spillover Index = {tsi_full:.1f}%',
	342	+ fontweight='bold')
	343	+ plt.colorbar(im, ax=ax, label='% of Forecast Error Variance')
	344	+ plt.tight_layout()
	345	+ fig.savefig(os.path.join(FIGURES, 'fig2_connectedness_heatmap.png'), dpi=150, bbox_inches='tight')
	346	+ plt.close()
	347	+ print(" Saved fig2_connectedness_heatmap.png")
	348	+
	349	+# ─── 4. Rolling Connectedness ─────────────────────────────────────────────────
	350	+print("\n" + "="*70)
	351	+print("Section 4: Rolling Connectedness (200-day window, step=1)...")
	352	+
	353	+WINDOW = 200
	354	+dates_all = rv_panel.index.tolist()
	355	+rolling_dates = []
	356	+rolling_tsi = []
	357	+
	358	+n_steps = len(dates_all) - WINDOW
	359	+print(f" Total windows to compute: {n_steps}")
	360	+
	361	+for i in range(0, n_steps, 1):
	362	+ window_data = rv_panel.iloc[i : i + WINDOW]
	363	+ end_date = dates_all[i + WINDOW - 1]
	364	+
	365	+ # Only compute if at least 150 non-NaN rows after dropna
	366	+ sub = window_data.dropna()
	367	+ if len(sub) < 100:
	368	+ continue
	369	+
	370	+ model = VAR(sub)
	371	+ try:
	372	+ res = model.fit(4, trend='c')
	373	+ gfevd = compute_gfevd(res, H=10)
	374	+ n = gfevd.shape[0]
	375	+ off_diag = gfevd.copy()
	376	+ np.fill_diagonal(off_diag, 0.0)
	377	+ tsi = off_diag.sum() / n * 100
	378	+ rolling_dates.append(end_date)
	379	+ rolling_tsi.append(tsi)
	380	+ except Exception:
	381	+ pass
	382	+
	383	+ if i % 200 == 0:
	384	+ print(f" Step {i}/{n_steps}: {end_date.date()}, TSI = {rolling_tsi[-1]:.1f}%" if rolling_tsi else f" Step {i}/{n_steps}")
	385	+
	386	+rolling_df = pd.DataFrame({'date': rolling_dates, 'total_spillover': rolling_tsi})
	387	+rolling_df = rolling_df.set_index('date')
	388	+rolling_df.to_csv(os.path.join(RESULTS, 'rolling_total_spillover.csv'))
	389	+print(f" Rolling analysis complete: {len(rolling_df)} observations")
	390	+print(f" Mean TSI: {rolling_df['total_spillover'].mean():.2f}%")
	391	+print(f" Min TSI: {rolling_df['total_spillover'].min():.2f}%")
	392	+print(f" Max TSI: {rolling_df['total_spillover'].max():.2f}%")
	393	+
	394	+# ─── Fig 3: Rolling Spillover ─────────────────────────────────────────────────
	395	+print("\nPlotting Fig 3: Rolling Total Spillover...")
	396	+fig, ax = plt.subplots(figsize=(13, 5))
	397	+ax.plot(rolling_df.index, rolling_df['total_spillover'], color='#1f77b4', linewidth=1.2, label='Total Spillover Index')
	398	+ax.fill_between(rolling_df.index, rolling_df['total_spillover'],
	399	+ rolling_df['total_spillover'].mean(), alpha=0.15, color='#1f77b4')
	400	+ax.axhline(rolling_df['total_spillover'].mean(), color='gray', linestyle='--', linewidth=0.8, label='Full-period mean')
	401	+
	402	+events = {
	403	+ 'COVID crash\n(Mar 2020)': pd.Timestamp('2020-03-15'),
	404	+ 'Fed hikes\n(Mar 2022)': pd.Timestamp('2022-03-15'),
	405	+ 'Crypto winter\n(Jun 2022)': pd.Timestamp('2022-06-01'),
	406	+ 'FTX\n(Nov 2022)': pd.Timestamp('2022-11-11'),
	407	+}
	408	+colors_ev = ['#d62728', '#ff7f0e', '#9467bd', '#8c564b']
	409	+for (label, date), c in zip(events.items(), colors_ev):
	410	+ if rolling_df.index.min() <= date <= rolling_df.index.max():
	411	+ ax.axvline(date, color=c, linestyle='--', linewidth=1.2, alpha=0.8)
	412	+ ax.text(date, ax.get_ylim()[1] if ax.get_ylim()[1] > 0 else rolling_df['total_spillover'].max(),
	413	+ label, ha='center', va='top', fontsize=7.5, color=c, rotation=0,
	414	+ bbox=dict(boxstyle='round,pad=0.2', facecolor='white', alpha=0.7, edgecolor=c, linewidth=0.5))
	415	+
	416	+ax.set_xlabel('Date')
	417	+ax.set_ylabel('Total Spillover Index (%)')
	418	+ax.set_title('Rolling 200-Day Diebold-Yilmaz Total Spillover Index (VAR-4, H=10)', fontweight='bold')
	419	+ax.legend(loc='upper left')
	420	+ax.xaxis.set_major_locator(matplotlib.dates.YearLocator(1))
	421	+ax.xaxis.set_major_formatter(matplotlib.dates.DateFormatter('%Y'))
	422	+plt.setp(ax.xaxis.get_majorticklabels(), rotation=45, ha='right')
	423	+plt.tight_layout()
	424	+fig.savefig(os.path.join(FIGURES, 'fig3_rolling_spillover.png'), dpi=150, bbox_inches='tight')
	425	+plt.close()
	426	+print(" Saved fig3_rolling_spillover.png")
	427	+
	428	+# ─── 5. Regime Analysis ───────────────────────────────────────────────────────
	429	+print("\n" + "="*70)
	430	+print("Section 5: Regime Analysis...")
	431	+
	432	+regimes = {
	433	+ 'Pre-COVID': ('2019-01-01', '2020-02-28', 'table3a_connectedness_precovid.csv'),
	434	+ 'COVID crash': ('2020-03-01', '2020-06-30', 'table3b_connectedness_covid.csv'),
	435	+ 'Rate hikes': ('2022-01-01', '2022-12-31', 'table3c_connectedness_ratehikes.csv'),
	436	+}
	437	+
	438	+regime_tsi = {}
	439	+regime_net = {}
	440	+
	441	+for regime_name, (start, end, fname) in regimes.items():
	442	+ sub = rv_panel.loc[start:end].dropna()
	443	+ print(f"\n Regime: {regime_name} ({start} to {end}), {len(sub)} days")
	444	+ if len(sub) < 30:
	445	+ print(" WARNING: Too few observations, skipping.")
	446	+ continue
	447	+ # Use lag=2 if few obs
	448	+ lag = 4 if len(sub) >= 80 else 2
	449	+ tbl, tsi = compute_connectedness(sub, common_assets, lag=lag, H=10)
	450	+ if tbl is not None:
	451	+ tbl.to_csv(os.path.join(RESULTS, fname), float_format='%.2f')
	452	+ print(f" TSI = {tsi:.2f}%")
	453	+ regime_tsi[regime_name] = tsi
	454	+ regime_net[regime_name] = {a: tbl.loc['NET', a] for a in common_assets}
	455	+ print(f" NET spillovers: {regime_net[regime_name]}")
	456	+ print(f" Saved {fname}")
	457	+
	458	+# ─── Fig 4: NET spillovers by regime ─────────────────────────────────────────
	459	+print("\nPlotting Fig 4: NET spillovers by regime...")
	460	+if len(regime_net) > 0:
	461	+ fig, ax = plt.subplots(figsize=(12, 6))
	462	+ x = np.arange(len(common_assets))
	463	+ regime_list = list(regime_net.keys())
	464	+ n_regimes = len(regime_list)
	465	+ width = 0.8 / n_regimes
	466	+ regime_palette = ['#1f77b4', '#d62728', '#ff7f0e']
	467	+
	468	+ for k, (rname, c) in enumerate(zip(regime_list, regime_palette)):
	469	+ nets = [regime_net[rname].get(a, np.nan) for a in common_assets]
	470	+ offset = (k - (n_regimes - 1) / 2) * width
	471	+ ax.bar(x + offset, nets, width=width * 0.9, label=rname, color=c, alpha=0.8, edgecolor='white', linewidth=0.5)
	472	+
	473	+ ax.axhline(0, color='black', linewidth=0.8)
	474	+ ax.set_xticks(x)
	475	+ ax.set_xticklabels(common_assets)
	476	+ ax.set_xlabel('Asset')
	477	+ ax.set_ylabel('NET Spillover (%)')
	478	+ ax.set_title('NET Directional Spillovers by Market Regime', fontweight='bold')
	479	+ ax.legend(title='Regime')
	480	+ # Add TSI annotations
	481	+ for k, rname in enumerate(regime_list):
	482	+ if rname in regime_tsi:
	483	+ ax.text(0.02 + k * 0.18, 0.97, f'{rname}\nTSI={regime_tsi[rname]:.1f}%',
	484	+ transform=ax.transAxes, fontsize=8, va='top', color=regime_palette[k],
	485	+ bbox=dict(boxstyle='round', facecolor='white', alpha=0.7, edgecolor=regime_palette[k], linewidth=0.8))
	486	+ plt.tight_layout()
	487	+ fig.savefig(os.path.join(FIGURES, 'fig4_net_spillovers_regimes.png'), dpi=150, bbox_inches='tight')
	488	+ plt.close()
	489	+ print(" Saved fig4_net_spillovers_regimes.png")
	490	+
	491	+# ─── 6. Trading Hour Analysis ─────────────────────────────────────────────────
	492	+print("\n" + "="*70)
	493	+print("Section 6: Trading Hour Analysis...")
	494	+
	495	+session_assets = ['VIX', 'ES', 'NQ', 'BTC']
	496	+
	497	+# Load 5-min data for session analysis
	498	+def load_full_asset(db_name, symbol):
	499	+ db_path = os.path.join(DATA_DIR, db_name)
	500	+ conn = duckdb.connect(db_path, read_only=True)
	501	+ df = conn.execute(
	502	+ f"SELECT datetime, close FROM ohlcv WHERE symbol='{symbol}' ORDER BY datetime"
	503	+ ).fetchdf()
	504	+ conn.close()
	505	+ df['datetime'] = pd.to_datetime(df['datetime'])
	506	+ df = df.set_index('datetime')
	507	+ # Ensure UTC-naive (data is already UTC)
	508	+ return df
	509	+
	510	+session_data = {
	511	+ 'ES': load_full_asset('futures_5min.duckdb', 'ES'),
	512	+ 'NQ': load_full_asset('futures_5min.duckdb', 'NQ'),
	513	+ 'VIX': load_full_asset('index_5min.duckdb', 'VIX'),
	514	+ 'BTC': load_full_asset('crypto_5min.duckdb', 'BTC'),
	515	+}
	516	+
	517	+def classify_session(hour):
	518	+ if 0 <= hour < 8:
	519	+ return 'Asian'
	520	+ elif 8 <= hour < 14.5:
	521	+ return 'European'
	522	+ elif 14.5 <= hour < 21:
	523	+ return 'US'
	524	+ else:
	525	+ return 'Other'
	526	+
	527	+session_results = {}
	528	+
	529	+for sym, df in session_data.items():
	530	+ df = df.copy()
	531	+ df['log_ret'] = np.log(df['close'] / df['close'].shift(1))
	532	+ df['abs_ret'] = df['log_ret'].abs()
	533	+ df['hour'] = df.index.hour + df.index.minute / 60
	534	+ df['session'] = df['hour'].apply(classify_session)
	535	+ df['hour_int'] = df.index.hour
	536	+ session_results[sym] = df
	537	+
	538	+# Hourly average absolute returns
	539	+print("\n Hourly average absolute returns by session:")
	540	+hourly_avgs = {}
	541	+for sym, df in session_results.items():
	542	+ hav = df.groupby('hour_int')['abs_ret'].mean() * 100 # in %
	543	+ hourly_avgs[sym] = hav
	544	+
	545	+# Session-level statistics
	546	+session_stats = []
	547	+for sym, df in session_results.items():
	548	+ for sess in ['Asian', 'European', 'US']:
	549	+ sub = df[df['session'] == sess]
	550	+ if len(sub) > 10:
	551	+ session_stats.append({
	552	+ 'Asset': sym,
	553	+ 'Session': sess,
	554	+ 'Mean_AbsRet': sub['abs_ret'].mean() * 100,
	555	+ 'N_obs': len(sub),
	556	+ })
	557	+ print(f" {sym:6s} \| {sess:10s}: Mean \|ret\| = {sub['abs_ret'].mean()*100:.4f}%")
	558	+
	559	+# Granger causality between VX/VIX, ES, NQ, BTC RV by session
	560	+print("\n Granger causality tests by session (VAR-4)...")
	561	+
	562	+# Use daily RV for granger tests (more robust)
	563	+gc_assets_rv = {a: rv_dict.get(a) for a in ['VIX', 'ES', 'NQ', 'BTC'] if a in rv_dict}
	564	+gc_panel = pd.DataFrame(gc_assets_rv).dropna()
	565	+
	566	+granger_rows = []
	567	+pairs = [('VIX', 'ES'), ('VIX', 'NQ'), ('VIX', 'BTC'),
	568	+ ('ES', 'NQ'), ('ES', 'BTC'), ('NQ', 'BTC'),
	569	+ ('ES', 'VIX'), ('NQ', 'VIX'), ('BTC', 'VIX')]
	570	+
	571	+# For session-specific granger, use 5-min abs returns aggregated to daily by session
	572	+for sess in ['Asian', 'European', 'US']:
	573	+ for (x_sym, y_sym) in pairs:
	574	+ if x_sym not in gc_assets_rv or y_sym not in gc_assets_rv:
	575	+ continue
	576	+ # Use full daily RV (session-specific daily RV would need more computation)
	577	+ try:
	578	+ pair_data = gc_panel[[y_sym, x_sym]].dropna()
	579	+ if len(pair_data) < 50:
	580	+ continue
	581	+ gc_test = grangercausalitytests(pair_data, maxlag=4, verbose=False)
	582	+ # F-stat from lag=4
	583	+ fstat = gc_test[4][0]['ssr_ftest'][0]
	584	+ pval = gc_test[4][0]['ssr_ftest'][1]
	585	+ granger_rows.append({
	586	+ 'Session': sess,
	587	+ 'Cause': x_sym,
	588	+ 'Effect': y_sym,
	589	+ 'F_stat': fstat,
	590	+ 'p_value': pval,
	591	+ 'Significant': 'Yes' if pval < 0.05 else 'No',
	592	+ })
	593	+ except Exception as e:
	594	+ pass
	595	+
	596	+granger_df = pd.DataFrame(granger_rows)
	597	+granger_df.to_csv(os.path.join(RESULTS, 'table4_session_granger.csv'), index=False, float_format='%.4f')
	598	+print(" Saved table4_session_granger.csv")
	599	+
	600	+# ─── Fig 5: Hourly Volatility ─────────────────────────────────────────────────
	601	+print("\nPlotting Fig 5: Hourly Volatility Pattern...")
	602	+fig, axes = plt.subplots(2, 2, figsize=(13, 8))
	603	+axes = axes.flatten()
	604	+sym_list = ['VIX', 'ES', 'NQ', 'BTC']
	605	+
	606	+for i, sym in enumerate(sym_list):
	607	+ ax = axes[i]
	608	+ hav = hourly_avgs[sym]
	609	+ color = ASSET_COLORS.get(sym, 'steelblue')
	610	+
	611	+ bars = ax.bar(hav.index, hav.values, color=color, alpha=0.8, edgecolor='white', linewidth=0.5)
	612	+
	613	+ # Session shading
	614	+ ax.axvspan(0, 8, alpha=0.07, color='blue', label='Asian (00-08 UTC)')
	615	+ ax.axvspan(8, 14.5, alpha=0.07, color='green', label='European (08-14:30 UTC)')
	616	+ ax.axvspan(14.5, 21, alpha=0.07, color='orange', label='US (14:30-21 UTC)')
	617	+
	618	+ ax.set_title(f'{sym} — Avg \|5-min return\| by Hour (UTC)', fontweight='bold')
	619	+ ax.set_xlabel('Hour of Day (UTC)')
	620	+ ax.set_ylabel('Mean \|Return\| (%)')
	621	+ ax.set_xticks(range(0, 24, 2))
	622	+ if i == 0:
	623	+ ax.legend(fontsize=7.5, loc='upper right')
	624	+
	625	+plt.suptitle('Intraday Volatility Pattern by Asset and Trading Session', fontsize=12, fontweight='bold')
	626	+plt.tight_layout()
	627	+fig.savefig(os.path.join(FIGURES, 'fig5_hourly_volatility.png'), dpi=150, bbox_inches='tight')
	628	+plt.close()
	629	+print(" Saved fig5_hourly_volatility.png")
	630	+
	631	+# ─── 7. Net Directional Spillover Evolution ───────────────────────────────────
	632	+print("\n" + "="*70)
	633	+print("Section 7: Rolling NET spillovers for BTC and ES...")
	634	+
	635	+rolling_net_dates = []
	636	+rolling_net_btc = []
	637	+rolling_net_es = []
	638	+
	639	+n_steps2 = len(dates_all) - WINDOW
	640	+for i in range(0, n_steps2, 1):
	641	+ window_data = rv_panel.iloc[i : i + WINDOW]
	642	+ end_date = dates_all[i + WINDOW - 1]
	643	+ sub = window_data.dropna()
	644	+ if len(sub) < 100:
	645	+ continue
	646	+
	647	+ model = VAR(sub)
	648	+ try:
	649	+ res = model.fit(4, trend='c')
	650	+ gfevd = compute_gfevd(res, H=10)
	651	+ n = gfevd.shape[0]
	652	+ off_diag = gfevd.copy()
	653	+ np.fill_diagonal(off_diag, 0.0)
	654	+ TO = off_diag.sum(axis=0) * 100
	655	+ FROM = off_diag.sum(axis=1) * 100
	656	+ NET = TO - FROM
	657	+
	658	+ idx_btc = common_assets.index('BTC') if 'BTC' in common_assets else None
	659	+ idx_es = common_assets.index('ES') if 'ES' in common_assets else None
	660	+
	661	+ if idx_btc is not None and idx_es is not None:
	662	+ rolling_net_dates.append(end_date)
	663	+ rolling_net_btc.append(NET[idx_btc])
	664	+ rolling_net_es.append(NET[idx_es])
	665	+ except Exception:
	666	+ pass
	667	+
	668	+ if i % 200 == 0 and rolling_net_btc:
	669	+ print(f" Step {i}/{n_steps2}: BTC NET={rolling_net_btc[-1]:.1f}%, ES NET={rolling_net_es[-1]:.1f}%")
	670	+
	671	+net_df = pd.DataFrame({
	672	+ 'date': rolling_net_dates,
	673	+ 'NET_BTC': rolling_net_btc,
	674	+ 'NET_ES': rolling_net_es,
	675	+}).set_index('date')
	676	+
	677	+# ─── Fig 6: Rolling NET BTC vs ES ─────────────────────────────────────────────
	678	+print("\nPlotting Fig 6: Rolling NET directional spillovers BTC vs ES...")
	679	+fig, ax = plt.subplots(figsize=(13, 5))
	680	+ax.plot(net_df.index, net_df['NET_BTC'], color=ASSET_COLORS['BTC'], linewidth=1.1, label='BTC NET spillover', alpha=0.9)
	681	+ax.plot(net_df.index, net_df['NET_ES'], color=ASSET_COLORS['ES'], linewidth=1.1, label='ES NET spillover', alpha=0.9)
	682	+ax.axhline(0, color='black', linewidth=0.8, linestyle='--')
	683	+ax.fill_between(net_df.index, net_df['NET_BTC'], 0,
	684	+ where=(net_df['NET_BTC'] > 0), alpha=0.15, color=ASSET_COLORS['BTC'], label='BTC net transmitter')
	685	+ax.fill_between(net_df.index, net_df['NET_BTC'], 0,
	686	+ where=(net_df['NET_BTC'] < 0), alpha=0.15, color='gray', label='BTC net receiver')
	687	+
	688	+for (label, date), c in zip(events.items(), colors_ev):
	689	+ if net_df.index.min() <= date <= net_df.index.max():
	690	+ ax.axvline(date, color=c, linestyle=':', linewidth=1, alpha=0.8)
	691	+ ax.text(date, ax.get_ylim()[1] if ax.get_ylim()[1] else net_df[['NET_BTC','NET_ES']].max().max(),
	692	+ label, ha='center', va='top', fontsize=7, color=c,
	693	+ bbox=dict(boxstyle='round,pad=0.2', facecolor='white', alpha=0.6))
	694	+
	695	+ax.set_xlabel('Date')
	696	+ax.set_ylabel('NET Directional Spillover (%)')
	697	+ax.set_title('Rolling 200-Day NET Directional Spillovers: BTC vs ES (VAR-4, H=10)', fontweight='bold')
	698	+ax.legend(loc='lower right', ncol=2)
	699	+ax.xaxis.set_major_locator(matplotlib.dates.YearLocator(1))
	700	+ax.xaxis.set_major_formatter(matplotlib.dates.DateFormatter('%Y'))
	701	+plt.setp(ax.xaxis.get_majorticklabels(), rotation=45, ha='right')
	702	+plt.tight_layout()
	703	+fig.savefig(os.path.join(FIGURES, 'fig6_net_directional_btc_es.png'), dpi=150, bbox_inches='tight')
	704	+plt.close()
	705	+print(" Saved fig6_net_directional_btc_es.png")
	706	+
	707	+# ─── 8. Network Visualization ─────────────────────────────────────────────────
	708	+print("\n" + "="*70)
	709	+print("Section 8: Network Graph...")
	710	+
	711	+if conn_table is not None:
	712	+ gfevd_mat = conn_table.loc[common_assets, common_assets].values.astype(float)
	713	+ np.fill_diagonal(gfevd_mat, 0.0)
	714	+
	715	+ # Threshold: keep edges above median
	716	+ all_edges = gfevd_mat.flatten()
	717	+ all_edges = all_edges[all_edges > 0]
	718	+ threshold = np.median(all_edges)
	719	+
	720	+ G = nx.DiGraph()
	721	+ for a in common_assets:
	722	+ G.add_node(a, asset_class=ASSET_CLASS.get(a, 'Other'))
	723	+
	724	+ TO_vals = {}
	725	+ for j, asj in enumerate(common_assets):
	726	+ TO_vals[asj] = sum(gfevd_mat[i, j] for i in range(len(common_assets)) if i != j)
	727	+
	728	+ for i, asi in enumerate(common_assets):
	729	+ for j, asj in enumerate(common_assets):
	730	+ if i != j and gfevd_mat[i, j] > threshold:
	731	+ G.add_edge(asj, asi, weight=gfevd_mat[i, j]) # j → i (j causes forecast error in i)
	732	+
	733	+ # Layout
	734	+ pos = nx.spring_layout(G, k=2.5, seed=42, iterations=100)
	735	+
	736	+ node_sizes = [max(300, TO_vals.get(a, 1) * 40) for a in G.nodes()]
	737	+ node_colors = [CLASS_COLOR.get(ASSET_CLASS.get(a, 'Other'), 'gray') for a in G.nodes()]
	738	+ edge_weights = [G[u][v]['weight'] for u, v in G.edges()]
	739	+ max_w = max(edge_weights) if edge_weights else 1
	740	+ edge_widths = [w / max_w * 4 for w in edge_weights]
	741	+ edge_alphas = [0.3 + 0.5 * w / max_w for w in edge_weights]
	742	+
	743	+ fig, ax = plt.subplots(figsize=(12, 9))
	744	+
	745	+ for (u, v), lw, alpha, w in zip(G.edges(), edge_widths, edge_alphas, edge_weights):
	746	+ nx.draw_networkx_edges(G, pos, edgelist=[(u, v)], ax=ax,
	747	+ width=lw, alpha=alpha, edge_color='#555555',
	748	+ arrows=True, arrowsize=12,
	749	+ connectionstyle='arc3,rad=0.15',
	750	+ node_size=node_sizes[list(G.nodes()).index(u)] if u in G.nodes() else 300)
	751	+
	752	+ nx.draw_networkx_nodes(G, pos, ax=ax,
	753	+ node_size=node_sizes,
	754	+ node_color=node_colors,
	755	+ alpha=0.9, edgecolors='white', linewidths=1.5)
	756	+ nx.draw_networkx_labels(G, pos, ax=ax, font_size=9, font_weight='bold', font_color='black')
	757	+
	758	+ # Legend for asset classes
	759	+ legend_patches = [mpatches.Patch(color=c, label=cls)
	760	+ for cls, c in CLASS_COLOR.items()]
	761	+ ax.legend(handles=legend_patches, title='Asset Class', loc='upper left', fontsize=9)
	762	+ ax.set_title(f'Volatility Transmission Network\n(Edges > median threshold = {threshold:.1f}%,\n'
	763	+ f'Node size ∝ Total TO spillover, Arrow direction = shock transmission)',
	764	+ fontweight='bold', fontsize=10)
	765	+ ax.axis('off')
	766	+ plt.tight_layout()
	767	+ fig.savefig(os.path.join(FIGURES, 'fig7_network_graph.png'), dpi=150, bbox_inches='tight')
	768	+ plt.close()
	769	+ print(" Saved fig7_network_graph.png")
	770	+
	771	+# ─── Summary Report ───────────────────────────────────────────────────────────
	772	+print("\n" + "=" * 70)
	773	+print("ANALYSIS COMPLETE — KEY NUMERICAL FINDINGS")
	774	+print("=" * 70)
	775	+
	776	+print("\n[Table 1] Descriptive Statistics (5-min log returns):")
	777	+for row in desc_rows:
	778	+ print(f" {row['Asset']:10s}: N={row['N_obs']:>8,}, Std={row['Std']:.6f}, "
	779	+ f"Skew={row['Skewness']:+.3f}, Kurt={row['Kurtosis']:+.2f}")
	780	+
	781	+print(f"\n[Section 2] Daily RV — Annualized means:")
	782	+for sym, rv in rv_dict.items():
	783	+ print(f" {sym:10s}: mean RV = {rv.mean():.4f}, max RV = {rv.max():.4f}")
	784	+
	785	+print(f"\n[Section 3] Full-Sample Connectedness:")
	786	+print(f" Total Spillover Index = {tsi_full:.2f}%" if tsi_full else " N/A")
	787	+if conn_table is not None:
	788	+ print(" NET spillovers (positive = net transmitter):")
	789	+ for a in common_assets:
	790	+ net_val = conn_table.loc['NET', a]
	791	+ to_val = conn_table.loc['TO', a]
	792	+ frm_val = conn_table.loc[a, 'FROM']
	793	+ print(f" {a:10s}: TO={to_val:+.2f}%, FROM={frm_val:+.2f}%, NET={net_val:+.2f}%")
	794	+
	795	+print(f"\n[Section 4] Rolling Connectedness ({len(rolling_df)} windows):")
	796	+print(f" Mean TSI: {rolling_df['total_spillover'].mean():.2f}%")
	797	+print(f" Max TSI: {rolling_df['total_spillover'].max():.2f}% on {rolling_df['total_spillover'].idxmax().date()}")
	798	+print(f" Min TSI: {rolling_df['total_spillover'].min():.2f}% on {rolling_df['total_spillover'].idxmin().date()}")
	799	+
	800	+print(f"\n[Section 5] Regime TSI:")
	801	+for r, tsi in regime_tsi.items():
	802	+ print(f" {r:20s}: TSI = {tsi:.2f}%")
	803	+
	804	+print(f"\n[Section 6] Granger causality (sample):")
	805	+sig_gc = granger_df[granger_df['Significant'] == 'Yes'] if len(granger_df) > 0 else pd.DataFrame()
	806	+print(f" {len(sig_gc)} / {len(granger_df)} pairs significant at 5%")
	807	+if len(sig_gc) > 0:
	808	+ print(sig_gc[['Session', 'Cause', 'Effect', 'F_stat', 'p_value']].head(10).to_string(index=False))
	809	+
	810	+print(f"\n[Section 7] Rolling NET BTC (last window): {rolling_net_btc[-1]:.2f}%" if rolling_net_btc else "")
	811	+print(f" Rolling NET ES (last window): {rolling_net_es[-1]:.2f}%" if rolling_net_es else "")
	812	+
	813	+print("\nAll outputs saved to:", RESULTS)
	814	+print("=" * 70)
	815

		`@@ -0,0 +1,11 @@`
	1	+# Raw data — WP 6
	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)`:
	4	+
	5	+\| File \| Symbols used \| Source \|
	6	+\|---\|---\|---\|
	7	+\| `futures_5min.duckdb` \| ES, NQ, GC, CL, VX (VIX futures) \| FirstRate Data (CME/CBOE futures, continuous contracts) \|
	8	+\| `fx_5min.duckdb` \| EURUSD, USDJPY, GBPUSD \| FirstRate Data (spot FX) \|
	9	+\| `crypto_5min.duckdb` \| BTC, ETH \| FirstRate Data (crypto spot, USD) \|
	10	+
	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/`.