WP41: main study results (2024), pairwise/subgroup/stress/economic analyses, phase 5 report, results section
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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docs/PHASE_4_REPORT.md
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| 1 | +# PHASE 4 — Scale: profiling, feasible Base architecture, main ingestion, frozen test protocol (2026-11-02) | |
| 2 | + | |
| 3 | +## Profiling (`scripts/benchmark.py`, M3U96b, Apple M3 Ultra, torch 2.15.0 MPS, FP32, real pilot grids) | |
| 4 | +Data loader (batch 64, memory-mapped grids, spawned workers, after warm-up): 3 971 ex/s (0 workers), 13 016 (4), 38 486 (8) | |
| 5 | +→ the loader is never the bottleneck (training consumes < 800 ex/s). | |
| 6 | + | |
| 7 | +| Preset | Parameters (measured) | Batch | Steps/s | Examples/s | Peak MPS memory | Inference ms/origin (batched) | | |
| 8 | +|---|---|---|---|---|---|---| | |
| 9 | +| Small (d192, 4L) | 3 455 619 | 32 / 64 / 128 | 20.8 / 12.2 / 5.9 | 666 / 782 / 758 | 54 / 69 / 97 MB | 0.34 / 0.25 / 0.27 | | |
| 10 | +| Spec (d256, 6L, the brief) | 7 677 955 | 32 / 64 / 128 | 11.5 / 6.3 / 3.0 | 369 / 402 / 380 | 114 / 119 / 147 MB | 0.59 / 0.48 / 0.53 | | |
| 11 | +| Base (d384, 8L) | 20 718 339 | 32 / 64 / 128 | 6.1 / 3.2 / 1.5 | 195 / 207 / 193 | 275 / 284 / 315 MB | 5.0 / 1.6 / 1.8 | | |
| 12 | +Batch-1 latency 4.3 / 5.1 / 5.9 ms. Losses finite in FP32 at every setting. Mixed precision was not enabled (no stability | |
| 13 | +study yet). Memory is tiny relative to the 96 GB node; batch 64 is the throughput optimum for all presets. | |
| 14 | + | |
| 15 | +## Decision: Base = 20.7 M parameters (inside the 15–30 M target); Small = 3.5 M (inside 3–5 M) | |
| 16 | +Budget at batch 64 for the frozen main protocol (12 000 steps = 768 000 examples ≈ 1.3 passes over the 600 k training | |
| 17 | +origins drawn at 2 per instrument-session): Small ≈ 16 min, Spec ≈ 32 min, Base ≈ 62 min of pure training plus | |
| 18 | +validation passes (60 batches every 1 000 steps) and prediction (≈ 1.45 M evaluation origins at stride 15 → ≈ 6 min | |
| 19 | +per Small model, ≈ 40 min for Base at 1.6 ms/origin). The 50–100 M "Large" preset is not trained in v1.0 | |
| 20 | +(no scaling evidence yet; documented limitation). | |
| 21 | + | |
| 22 | +## Main ingestion (completed before this phase, `docs/PHASE_1_REPORT.md`) | |
| 23 | +300 instruments × 2018–2025: 233 958 776 rows (220 142 835 regular hours), 3.5 GB Parquet, 414 s of exports, 19 s of | |
| 24 | +grids; disk usage ≈ 8 GB of 423 GB free. | |
| 25 | + | |
| 26 | +## Frozen test protocol (`configs/main.yaml`, `configs/final.yaml`) | |
| 27 | +- Train ≤ 2022-12-31, validation 2023, development test 2024 (model selection and ablations), final 2025 untouched | |
| 28 | + (run once with the main-study checkpoints, `--models-from results/metrics/main`). | |
| 29 | +- Evaluation origins every 15 minutes from 10:00 (24 per normal session); 200 Monte Carlo draws per origin. | |
| 30 | +- Held-out instruments (60) evaluated zero-shot with the pooled checkpoints. | |
| 31 | +- Ablations (`configs/ablations.yaml`): Small scale, 4 000 steps for every variant **and** for its reference | |
| 32 | + (`mrpt_small_b4k`), seed 1 (+ seeds 2, 3 for the reference). | |
| 33 | +- Statistics: day-cluster bootstrap, HAC Diebold–Mariano with lag = overlap × instruments, Holm/BH. | |
| 34 | + | |
| 35 | +## Go / no-go | |
| 36 | +GO to P5 (`main_chain` launched on M3U96b 2026-11-02 18:5x ET: benchmark → `configs/main.yaml`). | |
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| 1 | +# PHASE 5 — Main experiments (development test 2024) — 2026-11-02/03 | |
| 2 | + | |
| 3 | +## Run (`configs/main.yaml`, M3U96b, launched 19:02 ET, finished 23:06 ET; `results/logs/main_chain.out`) | |
| 4 | +- 240 pooled instruments, 2018-01-02 → 2025-12-31 grids; origins: train 586 202 (2 per instrument-session, 2018–2022), | |
| 5 | + validation 1 040 345 (2023, stride 15), **test 986 468 (2024, stride 15)**, final 1 008 425 (2025, untouched). | |
| 6 | +- Baselines stage: origin frames 153 s (test) + train; fits + scoring 1 581 s total for 8 baselines. | |
| 7 | +- Neural stage (batch 64, 12 000 steps = 768 000 examples, seed 1, early stopping on validation NLL every 1 000 steps, patience 4): | |
| 8 | + | |
| 9 | +| Model | Params | Train+predict wall | Best val NLL | Examples/s (train, incl. validation) | | |
| 10 | +|---|---|---|---|---| | |
| 11 | +| MRPT-S (A+B+C) | 3 455 619 | 2 372 s | −6.4535 | ≈ 450 | | |
| 12 | +| MRPT-S (A only) | 3 200 259 | 1 509 s | −6.4520 | ≈ 600 | | |
| 13 | +| MRPT-B (A+B+C) | 20 718 339 | 6 684 s | −6.4526 | ≈ 180 | | |
| 14 | +| TCN (A) | 231 459 | 1 329 s | −6.4518 | | | |
| 15 | +| MLP (A, last 60 bars) | 301 827 | 1 219 s | −6.4497 | | | |
| 16 | +All five reached the full 12 000 steps (no early stop); validation NLL plateaued from ≈ 7 000 steps for MRPT-S. | |
| 17 | + | |
| 18 | +## Headline scores (scaled CRPS of the cumulative return; day-cluster 95 % CI; `leaderboard_test.csv`) | |
| 19 | +| Model | H=5 | H=15 | H=30 | H=60 | Δ vs random walk (H=5 / 60) | | |
| 20 | +|---|---|---|---|---|---| | |
| 21 | +| Random walk | 0.4699 [0.4648, 0.4754] | 0.4575 | 0.4469 | 0.4347 [0.4271, 0.4441] | — | | |
| 22 | +| EWMA-t | 0.4547 | 0.4425 | 0.4326 | 0.4214 | −3.65 % / −3.47 % | | |
| 23 | +| GARCH(1,1)-t | 0.4558 | 0.4430 | 0.4333 | 0.4232 | −3.60 % / −3.40 % | | |
| 24 | +| HAR-RV | 0.4615 | 0.4403 | 0.4295 | **0.4166** | −2.19 % / **−4.89 %** | | |
| 25 | +| Ridge / elastic net | 0.4603 | 0.4405 | 0.4297 | 0.4167 | −2.88 % / −4.89 % | | |
| 26 | +| LightGBM | 0.4591 | 0.4415 | 0.4293 | 0.4166 | −2.88 % / −4.85 % | | |
| 27 | +| MLP (1m) | 0.4538 | 0.4421 | 0.4319 | 0.4197 | −3.94 % / −4.07 % | | |
| 28 | +| TCN (1m) | 0.4538 | 0.4427 | 0.4327 | 0.4207 | −3.93 % / −3.73 % | | |
| 29 | +| MRPT-S 1m only | 0.4533 | 0.4416 | 0.4314 | 0.4192 | −4.02 % / −4.17 % | | |
| 30 | +| **MRPT-S multi-res.** | **0.4531** | **0.4414** | **0.4311** | 0.4187 | −4.05 % / −4.27 % | | |
| 31 | +| MRPT-B multi-res. | 0.4532 | 0.4414 | 0.4312 | 0.4189 | −4.04 % / −4.23 % | | |
| 32 | +Every model beats the random walk (DM t between −25 and −72, all p < 1e-10 after Holm). | |
| 33 | + | |
| 34 | +## Pre-specified contrasts (`pairwise_test.csv`; relative CRPS change, DM-HAC t, Holm-adjusted p) | |
| 35 | +| Contrast | H=5 | H=15 | H=30 | H=60 | | |
| 36 | +|---|---|---|---|---| | |
| 37 | +| **H1** MRPT-S multi-res vs 1m-only | −0.04 % (t −5.3) | −0.04 % (t −4.5) | −0.05 % (t −4.5) | −0.10 % (t −5.3) | | |
| 38 | +| MRPT-B vs MRPT-S | +0.01 % (t 1.6, p 0.35) | −0.01 % (t −1.3) | −0.01 % (t −0.8) | +0.04 % (t 2.3, p 0.10) | | |
| 39 | +| MRPT-S vs HAR-RV | −1.91 % (t −58) | +0.34 % (t 12) | +0.53 % (t 12) | +0.65 % (t 10) | | |
| 40 | +| MRPT-S vs GARCH-t | −0.47 % (t −16) | −0.27 % (t −9) | −0.37 % (t −11) | −0.90 % (t −19) | | |
| 41 | +| MRPT-S vs EWMA-t | −0.42 % | −0.35 % | −0.47 % | −0.83 % | | |
| 42 | +| MRPT-S vs LightGBM | −1.21 % (t −22) | +0.09 % (t 2.0, p 0.19) | +0.53 % (t 12) | +0.61 % (t 10) | | |
| 43 | +| MRPT-S vs TCN | −0.13 % | −0.29 % | −0.39 % | −0.56 % | | |
| 44 | +| MRPT-S vs MLP | −0.12 % | −0.11 % | −0.12 % | −0.21 % | | |
| 45 | +Reading: H1 is statistically detectable but economically negligible (a tenth of a percent of CRPS at 60 minutes). | |
| 46 | +Model size does not matter (Base ≈ Small). The neural family wins at 5 minutes; the feature-based volatility | |
| 47 | +regressions (HAR-RV, ridge, LightGBM) win from 15 minutes on, by 0.3–0.7 %. | |
| 48 | + | |
| 49 | +## Calibration (`leaderboard_test.csv`, `stress_calibration_test.csv`) | |
| 50 | +Neural models and GARCH/EWMA are over-dispersed in the centre (50 % coverage 0.55–0.59, PIT KS 0.03–0.05) and | |
| 51 | +near nominal at 95 %; HAR-RV / ridge / LightGBM are close to nominal from 15 minutes (0.49 / 0.80 / 0.96 at 60 min, | |
| 52 | +KS 0.008) but badly under-dispersed at 5 minutes (50 % coverage 0.37, 95 % coverage 0.90). On stress days (top | |
| 53 | +decile of cross-sectional σ_t, 100 846 origins) MRPT-S keeps 0.57 / 0.85 / 0.97 coverage (normal days 0.58 / 0.85 / 0.96): | |
| 54 | +calibration does not deteriorate under stress, but the regime-conditioning hypothesis (H3) is tested in the ablations. | |
| 55 | + | |
| 56 | +## Subgroups (MRPT-S vs HAR-RV at H=60, `subgroups_mrpt_small_vs_har_rv_test.csv`) | |
| 57 | +HAR-RV's advantage concentrates in low-ADV stocks (+1.3 %), low-volatility instruments (+1.0 %), transport/utilities | |
| 58 | +(+1.9 %), fixed-income ETFs (+1.8 %) and the "unknown"-sector group (+2.8 %); MRPT-S is better on broad-equity, | |
| 59 | +sector and volatility ETFs (−0.3 to −1.1 %) and on high-ADV instruments (−0.03 %, n.s.). Afternoon origins favour HAR (+1.0 %). | |
| 60 | + | |
| 61 | +## Economic content (H5, exploratory; `economic_test.csv`) | |
| 62 | +Correlation between the predictive median and the realised 60-minute return: 0.003 (MRPT-S), 0.025 (MRPT-B), 0.014 (TCN), | |
| 63 | +0.007 (MLP); regression slopes between −1 and 1.2; the median's typical magnitude is 0.06–0.7 bp. With a 1 bp | |
| 64 | +round-trip cost MRPT-S trades 17 % of origins at 60 minutes for a net −0.00 bp [−1.7, +1.8]; with 2.5–10 bp costs the | |
| 65 | +traded share collapses below 4 % and every net return interval contains zero. **No evidence of economic content.** | |
| 66 | + | |
| 67 | +## Artifacts | |
| 68 | +`results/metrics/main/`: `summary_*_test.json`, `per_origin_*_test.npz` (node + laptop, not committed), `leaderboard_test.csv`, | |
| 69 | +`compare_{crps,wis,qlike}_vs_naive_rw_test.csv`, `pairwise_test.csv`, `subgroups_*.csv`, `stress_calibration_test.csv`, | |
| 70 | +`economic_test.csv`, `<model>/train_log.jsonl`, `train_summary.json`, `best.pt` (node only). Tables and figures: | |
| 71 | +`paper/tables/main_*.tex`, `paper/figures/fig_main_*`. | |
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| 131 | +\newcommand{\relpilotmlpwisHonefive}{-3.15} | |
| 132 | +\newcommand{\dmrelpilotmlpwisHonefive}{-8.3} | |
| 133 | +\newcommand{\relpilotmlpwisHthreezero}{-3.23} | |
| 134 | +\newcommand{\dmrelpilotmlpwisHthreezero}{-7.3} | |
| 135 | +\newcommand{\relpilotmlpwisHsixzero}{-2.59} | |
| 136 | +\newcommand{\dmrelpilotmlpwisHsixzero}{-4.1} | |
| 137 | +\newcommand{\relpilotmrptsmallonemonlywisHfive}{-3.13} | |
| 138 | +\newcommand{\dmrelpilotmrptsmallonemonlywisHfive}{-8.7} | |
| 139 | +\newcommand{\relpilotmrptsmallonemonlywisHonefive}{-3.20} | |
| 140 | +\newcommand{\dmrelpilotmrptsmallonemonlywisHonefive}{-7.9} | |
| 141 | +\newcommand{\relpilotmrptsmallonemonlywisHthreezero}{-3.39} | |
| 142 | +\newcommand{\dmrelpilotmrptsmallonemonlywisHthreezero}{-6.9} | |
| 143 | +\newcommand{\relpilotmrptsmallonemonlywisHsixzero}{-2.53} | |
| 144 | +\newcommand{\dmrelpilotmrptsmallonemonlywisHsixzero}{-3.8} | |
| 145 | +\newcommand{\relpilotmrptsmallwisHfive}{-3.13} | |
| 146 | +\newcommand{\dmrelpilotmrptsmallwisHfive}{-8.7} | |
| 147 | +\newcommand{\relpilotmrptsmallwisHonefive}{-3.29} | |
| 148 | +\newcommand{\dmrelpilotmrptsmallwisHonefive}{-8.1} | |
| 149 | +\newcommand{\relpilotmrptsmallwisHthreezero}{-3.57} | |
| 150 | +\newcommand{\dmrelpilotmrptsmallwisHthreezero}{-7.3} | |
| 151 | +\newcommand{\relpilotmrptsmallwisHsixzero}{-2.78} | |
| 152 | +\newcommand{\dmrelpilotmrptsmallwisHsixzero}{-4.2} | |
| 153 | +\newcommand{\relpilotridgewisHfive}{-2.06} | |
| 154 | +\newcommand{\dmrelpilotridgewisHfive}{-3.4} | |
| 155 | +\newcommand{\relpilotridgewisHonefive}{-3.26} | |
| 156 | +\newcommand{\dmrelpilotridgewisHonefive}{-5.8} | |
| 157 | +\newcommand{\relpilotridgewisHthreezero}{-3.55} | |
| 158 | +\newcommand{\dmrelpilotridgewisHthreezero}{-5.7} | |
| 159 | +\newcommand{\relpilotridgewisHsixzero}{-3.14} | |
| 160 | +\newcommand{\dmrelpilotridgewisHsixzero}{-4.2} | |
| 161 | +\newcommand{\relpilotseasonalvolwisHfive}{-1.98} | |
| 162 | +\newcommand{\dmrelpilotseasonalvolwisHfive}{-5.1} | |
| 163 | +\newcommand{\relpilotseasonalvolwisHonefive}{-2.60} | |
| 164 | +\newcommand{\dmrelpilotseasonalvolwisHonefive}{-6.2} | |
| 165 | +\newcommand{\relpilotseasonalvolwisHthreezero}{-2.77} | |
| 166 | +\newcommand{\dmrelpilotseasonalvolwisHthreezero}{-5.3} | |
| 167 | +\newcommand{\relpilotseasonalvolwisHsixzero}{-2.12} | |
| 168 | +\newcommand{\dmrelpilotseasonalvolwisHsixzero}{-3.1} | |
| 169 | +\newcommand{\relpilottcnwisHfive}{-3.25} | |
| 170 | +\newcommand{\dmrelpilottcnwisHfive}{-9.7} | |
| 171 | +\newcommand{\relpilottcnwisHonefive}{-3.15} | |
| 172 | +\newcommand{\dmrelpilottcnwisHonefive}{-7.9} | |
| 173 | +\newcommand{\relpilottcnwisHthreezero}{-3.41} | |
| 174 | +\newcommand{\dmrelpilottcnwisHthreezero}{-7.4} | |
| 175 | +\newcommand{\relpilottcnwisHsixzero}{-2.64} | |
| 176 | +\newcommand{\dmrelpilottcnwisHsixzero}{-3.9} | |
| 177 | +\newcommand{\relpilotelasticnetqlikeHfive}{-2906922453727.77} | |
| 178 | +\newcommand{\dmrelpilotelasticnetqlikeHfive}{-1.4} | |
| 179 | +\newcommand{\relpilotelasticnetqlikeHonefive}{-14052357953211.58} | |
| 180 | +\newcommand{\dmrelpilotelasticnetqlikeHonefive}{-11.7} | |
| 181 | +\newcommand{\relpilotelasticnetqlikeHthreezero}{-13800380130330.72} | |
| 182 | +\newcommand{\dmrelpilotelasticnetqlikeHthreezero}{-9.9} | |
| 183 | +\newcommand{\relpilotelasticnetqlikeHsixzero}{-13480669954535.19} | |
| 184 | +\newcommand{\dmrelpilotelasticnetqlikeHsixzero}{-8.2} | |
| 185 | +\newcommand{\relpilotewmaqlikeHfive}{-12554922968119.03} | |
| 186 | +\newcommand{\dmrelpilotewmaqlikeHfive}{-8.8} | |
| 187 | +\newcommand{\relpilotewmaqlikeHonefive}{-11610326741044.22} | |
| 188 | +\newcommand{\dmrelpilotewmaqlikeHonefive}{-8.6} | |
| 189 | +\newcommand{\relpilotewmaqlikeHthreezero}{-9962403507408.67} | |
| 190 | +\newcommand{\dmrelpilotewmaqlikeHthreezero}{-6.7} | |
| 191 | +\newcommand{\relpilotewmaqlikeHsixzero}{-7537309379639.13} | |
| 192 | +\newcommand{\dmrelpilotewmaqlikeHsixzero}{-3.7} | |
| 193 | +\newcommand{\relpilotgarchtqlikeHfive}{-6845837520747.71} | |
| 194 | +\newcommand{\dmrelpilotgarchtqlikeHfive}{-5.6} | |
| 195 | +\newcommand{\relpilotgarchtqlikeHonefive}{-4710411807615.16} | |
| 196 | +\newcommand{\dmrelpilotgarchtqlikeHonefive}{-4.2} | |
| 197 | +\newcommand{\relpilotgarchtqlikeHthreezero}{-1671497472176.46} | |
| 198 | +\newcommand{\dmrelpilotgarchtqlikeHthreezero}{-1.3} | |
| 199 | +\newcommand{\relpilotgarchtqlikeHsixzero}{+4026232839171.85} | |
| 200 | +\newcommand{\dmrelpilotgarchtqlikeHsixzero}{2.9} | |
| 201 | +\newcommand{\relpilotharrvqlikeHfive}{+7877866372961.78} | |
| 202 | +\newcommand{\dmrelpilotharrvqlikeHfive}{4.6} | |
| 203 | +\newcommand{\relpilotharrvqlikeHonefive}{-14099293226631.73} | |
| 204 | +\newcommand{\dmrelpilotharrvqlikeHonefive}{-13.0} | |
| 205 | +\newcommand{\relpilotharrvqlikeHthreezero}{-13394448504861.81} | |
| 206 | +\newcommand{\dmrelpilotharrvqlikeHthreezero}{-10.4} | |
| 207 | +\newcommand{\relpilotharrvqlikeHsixzero}{-12560029461854.98} | |
| 208 | +\newcommand{\dmrelpilotharrvqlikeHsixzero}{-8.0} | |
| 209 | +\newcommand{\relpilotlightgbmqlikeHfive}{+80780260086423.78} | |
| 210 | +\newcommand{\dmrelpilotlightgbmqlikeHfive}{1.4} | |
| 211 | +\newcommand{\relpilotlightgbmqlikeHonefive}{-12012831272926.51} | |
| 212 | +\newcommand{\dmrelpilotlightgbmqlikeHonefive}{-7.3} | |
| 213 | +\newcommand{\relpilotlightgbmqlikeHthreezero}{-12181626304741.97} | |
| 214 | +\newcommand{\dmrelpilotlightgbmqlikeHthreezero}{-7.1} | |
| 215 | +\newcommand{\relpilotlightgbmqlikeHsixzero}{-11572312577415.51} | |
| 216 | +\newcommand{\dmrelpilotlightgbmqlikeHsixzero}{-6.0} | |
| 217 | +\newcommand{\relpilotmlpqlikeHfive}{-13608727182964.57} | |
| 218 | +\newcommand{\dmrelpilotmlpqlikeHfive}{-13.2} | |
| 219 | +\newcommand{\relpilotmlpqlikeHonefive}{-13379373428123.78} | |
| 220 | +\newcommand{\dmrelpilotmlpqlikeHonefive}{-13.6} | |
| 221 | +\newcommand{\relpilotmlpqlikeHthreezero}{-13042336995340.29} | |
| 222 | +\newcommand{\dmrelpilotmlpqlikeHthreezero}{-11.2} | |
| 223 | +\newcommand{\relpilotmlpqlikeHsixzero}{-12126414938724.40} | |
| 224 | +\newcommand{\dmrelpilotmlpqlikeHsixzero}{-8.1} | |
| 225 | +\newcommand{\relpilotmrptsmallonemonlyqlikeHfive}{-13769052086011.91} | |
| 226 | +\newcommand{\dmrelpilotmrptsmallonemonlyqlikeHfive}{-11.5} | |
| 227 | +\newcommand{\relpilotmrptsmallonemonlyqlikeHonefive}{-13594106578801.23} | |
| 228 | +\newcommand{\dmrelpilotmrptsmallonemonlyqlikeHonefive}{-13.2} | |
| 229 | +\newcommand{\relpilotmrptsmallonemonlyqlikeHthreezero}{-12903146151897.46} | |
| 230 | +\newcommand{\dmrelpilotmrptsmallonemonlyqlikeHthreezero}{-11.4} | |
| 231 | +\newcommand{\relpilotmrptsmallonemonlyqlikeHsixzero}{-12091461273483.05} | |
| 232 | +\newcommand{\dmrelpilotmrptsmallonemonlyqlikeHsixzero}{-8.3} | |
| 233 | +\newcommand{\relpilotmrptsmallqlikeHfive}{-14426818050181.94} | |
| 234 | +\newcommand{\dmrelpilotmrptsmallqlikeHfive}{-11.8} | |
| 235 | +\newcommand{\relpilotmrptsmallqlikeHonefive}{-14161537101518.33} | |
| 236 | +\newcommand{\dmrelpilotmrptsmallqlikeHonefive}{-13.4} | |
| 237 | +\newcommand{\relpilotmrptsmallqlikeHthreezero}{-13449231005232.20} | |
| 238 | +\newcommand{\dmrelpilotmrptsmallqlikeHthreezero}{-12.1} | |
| 239 | +\newcommand{\relpilotmrptsmallqlikeHsixzero}{-12662443344111.06} | |
| 240 | +\newcommand{\dmrelpilotmrptsmallqlikeHsixzero}{-9.2} | |
| 241 | +\newcommand{\relpilotridgeqlikeHfive}{-2945713870141.00} | |
| 242 | +\newcommand{\dmrelpilotridgeqlikeHfive}{-1.4} | |
| 243 | +\newcommand{\relpilotridgeqlikeHonefive}{-14078646030114.02} | |
| 244 | +\newcommand{\dmrelpilotridgeqlikeHonefive}{-11.7} | |
| 245 | +\newcommand{\relpilotridgeqlikeHthreezero}{-13850072137900.00} | |
| 246 | +\newcommand{\dmrelpilotridgeqlikeHthreezero}{-9.9} | |
| 247 | +\newcommand{\relpilotridgeqlikeHsixzero}{-13521968596908.26} | |
| 248 | +\newcommand{\dmrelpilotridgeqlikeHsixzero}{-8.3} | |
| 249 | +\newcommand{\relpilotseasonalvolqlikeHfive}{-6631047621301.96} | |
| 250 | +\newcommand{\dmrelpilotseasonalvolqlikeHfive}{-3.7} | |
| 251 | +\newcommand{\relpilotseasonalvolqlikeHonefive}{-9798545943930.17} | |
| 252 | +\newcommand{\dmrelpilotseasonalvolqlikeHonefive}{-6.7} | |
| 253 | +\newcommand{\relpilotseasonalvolqlikeHthreezero}{-8922777889662.27} | |
| 254 | +\newcommand{\dmrelpilotseasonalvolqlikeHthreezero}{-5.8} | |
| 255 | +\newcommand{\relpilotseasonalvolqlikeHsixzero}{-8074565519238.53} | |
| 256 | +\newcommand{\dmrelpilotseasonalvolqlikeHsixzero}{-4.6} | |
| 257 | +\newcommand{\relpilottcnqlikeHfive}{-13969630443261.25} | |
| 258 | +\newcommand{\dmrelpilottcnqlikeHfive}{-13.3} | |
| 259 | +\newcommand{\relpilottcnqlikeHonefive}{-13939960177831.86} | |
| 260 | +\newcommand{\dmrelpilottcnqlikeHonefive}{-13.9} | |
| 261 | +\newcommand{\relpilottcnqlikeHthreezero}{-13400649669390.51} | |
| 262 | +\newcommand{\dmrelpilottcnqlikeHthreezero}{-12.0} | |
| 263 | +\newcommand{\relpilottcnqlikeHsixzero}{-12492078176605.08} | |
| 264 | +\newcommand{\dmrelpilottcnqlikeHsixzero}{-8.7} | |
| 265 | +\newcommand{\crpspilotelasticnetHfive}{0.4732} | |
| 266 | +\newcommand{\covfiftypilotelasticnetHfive}{41} | |
| 267 | +\newcommand{\covninetyfivepilotelasticnetHfive}{91.3} | |
| 268 | +\newcommand{\crpspilotelasticnetHonefive}{0.4764} | |
| 269 | +\newcommand{\covfiftypilotelasticnetHonefive}{44} | |
| 270 | +\newcommand{\covninetyfivepilotelasticnetHonefive}{93.8} | |
| 271 | +\newcommand{\crpspilotelasticnetHthreezero}{0.4841} | |
| 272 | +\newcommand{\covfiftypilotelasticnetHthreezero}{44} | |
| 273 | +\newcommand{\covninetyfivepilotelasticnetHthreezero}{94.1} | |
| 274 | +\newcommand{\crpspilotelasticnetHsixzero}{0.4725} | |
| 275 | +\newcommand{\covfiftypilotelasticnetHsixzero}{46} | |
| 276 | +\newcommand{\covninetyfivepilotelasticnetHsixzero}{93.8} | |
| 277 | +\newcommand{\crpspilotewmaHfive}{0.4699} | |
| 278 | +\newcommand{\covfiftypilotewmaHfive}{51} | |
| 279 | +\newcommand{\covninetyfivepilotewmaHfive}{96.6} | |
| 280 | +\newcommand{\crpspilotewmaHonefive}{0.4775} | |
| 281 | +\newcommand{\covfiftypilotewmaHonefive}{50} | |
| 282 | +\newcommand{\covninetyfivepilotewmaHonefive}{96.4} | |
| 283 | +\newcommand{\crpspilotewmaHthreezero}{0.4868} | |
| 284 | +\newcommand{\covfiftypilotewmaHthreezero}{49} | |
| 285 | +\newcommand{\covninetyfivepilotewmaHthreezero}{95.9} | |
| 286 | +\newcommand{\crpspilotewmaHsixzero}{0.4773} | |
| 287 | +\newcommand{\covfiftypilotewmaHsixzero}{51} | |
| 288 | +\newcommand{\covninetyfivepilotewmaHsixzero}{95.7} | |
| 289 | +\newcommand{\crpspilotgarchtHfive}{0.4714} | |
| 290 | +\newcommand{\covfiftypilotgarchtHfive}{54} | |
| 291 | +\newcommand{\covninetyfivepilotgarchtHfive}{97.4} | |
| 292 | +\newcommand{\crpspilotgarchtHonefive}{0.4783} | |
| 293 | +\newcommand{\covfiftypilotgarchtHonefive}{56} | |
| 294 | +\newcommand{\covninetyfivepilotgarchtHonefive}{98.0} | |
| 295 | +\newcommand{\crpspilotgarchtHthreezero}{0.4876} | |
| 296 | +\newcommand{\covfiftypilotgarchtHthreezero}{56} | |
| 297 | +\newcommand{\covninetyfivepilotgarchtHthreezero}{98.0} | |
| 298 | +\newcommand{\crpspilotgarchtHsixzero}{0.4789} | |
| 299 | +\newcommand{\covfiftypilotgarchtHsixzero}{59} | |
| 300 | +\newcommand{\covninetyfivepilotgarchtHsixzero}{98.0} | |
| 301 | +\newcommand{\crpspilotharrvHfive}{0.4833} | |
| 302 | +\newcommand{\covfiftypilotharrvHfive}{63} | |
| 303 | +\newcommand{\covninetyfivepilotharrvHfive}{99.2} | |
| 304 | +\newcommand{\crpspilotharrvHonefive}{0.4761} | |
| 305 | +\newcommand{\covfiftypilotharrvHonefive}{48} | |
| 306 | +\newcommand{\covninetyfivepilotharrvHonefive}{95.9} | |
| 307 | +\newcommand{\crpspilotharrvHthreezero}{0.4845} | |
| 308 | +\newcommand{\covfiftypilotharrvHthreezero}{46} | |
| 309 | +\newcommand{\covninetyfivepilotharrvHthreezero}{95.0} | |
| 310 | +\newcommand{\crpspilotharrvHsixzero}{0.4728} | |
| 311 | +\newcommand{\covfiftypilotharrvHsixzero}{48} | |
| 312 | +\newcommand{\covninetyfivepilotharrvHsixzero}{94.8} | |
| 313 | +\newcommand{\crpspilotlightgbmHfive}{0.5090} | |
| 314 | +\newcommand{\covfiftypilotlightgbmHfive}{35} | |
| 315 | +\newcommand{\covninetyfivepilotlightgbmHfive}{89.2} | |
| 316 | +\newcommand{\crpspilotlightgbmHonefive}{0.5034} | |
| 317 | +\newcommand{\covfiftypilotlightgbmHonefive}{41} | |
| 318 | +\newcommand{\covninetyfivepilotlightgbmHonefive}{92.1} | |
| 319 | +\newcommand{\crpspilotlightgbmHthreezero}{0.5116} | |
| 320 | +\newcommand{\covfiftypilotlightgbmHthreezero}{46} | |
| 321 | +\newcommand{\covninetyfivepilotlightgbmHthreezero}{92.4} | |
| 322 | +\newcommand{\crpspilotlightgbmHsixzero}{0.5019} | |
| 323 | +\newcommand{\covfiftypilotlightgbmHsixzero}{45} | |
| 324 | +\newcommand{\covninetyfivepilotlightgbmHsixzero}{92.1} | |
| 325 | +\newcommand{\crpspilotmlpHfive}{0.4689} | |
| 326 | +\newcommand{\covfiftypilotmlpHfive}{51} | |
| 327 | +\newcommand{\covninetyfivepilotmlpHfive}{95.3} | |
| 328 | +\newcommand{\crpspilotmlpHonefive}{0.4769} | |
| 329 | +\newcommand{\covfiftypilotmlpHonefive}{53} | |
| 330 | +\newcommand{\covninetyfivepilotmlpHonefive}{94.7} | |
| 331 | +\newcommand{\crpspilotmlpHthreezero}{0.4847} | |
| 332 | +\newcommand{\covfiftypilotmlpHthreezero}{51} | |
| 333 | +\newcommand{\covninetyfivepilotmlpHthreezero}{94.3} | |
| 334 | +\newcommand{\crpspilotmlpHsixzero}{0.4743} | |
| 335 | +\newcommand{\covfiftypilotmlpHsixzero}{53} | |
| 336 | +\newcommand{\covninetyfivepilotmlpHsixzero}{94.1} | |
| 337 | +\newcommand{\crpspilotmrptsmallonemonlyHfive}{0.4693} | |
| 338 | +\newcommand{\covfiftypilotmrptsmallonemonlyHfive}{55} | |
| 339 | +\newcommand{\covninetyfivepilotmrptsmallonemonlyHfive}{96.5} | |
| 340 | +\newcommand{\crpspilotmrptsmallonemonlyHonefive}{0.4765} | |
| 341 | +\newcommand{\covfiftypilotmrptsmallonemonlyHonefive}{56} | |
| 342 | +\newcommand{\covninetyfivepilotmrptsmallonemonlyHonefive}{96.0} | |
| 343 | +\newcommand{\crpspilotmrptsmallonemonlyHthreezero}{0.4842} | |
| 344 | +\newcommand{\covfiftypilotmrptsmallonemonlyHthreezero}{53} | |
| 345 | +\newcommand{\covninetyfivepilotmrptsmallonemonlyHthreezero}{95.2} | |
| 346 | +\newcommand{\crpspilotmrptsmallonemonlyHsixzero}{0.4745} | |
| 347 | +\newcommand{\covfiftypilotmrptsmallonemonlyHsixzero}{54} | |
| 348 | +\newcommand{\covninetyfivepilotmrptsmallonemonlyHsixzero}{94.8} | |
| 349 | +\newcommand{\crpspilotmrptsmallHfive}{0.4697} | |
| 350 | +\newcommand{\covfiftypilotmrptsmallHfive}{54} | |
| 351 | +\newcommand{\covninetyfivepilotmrptsmallHfive}{96.3} | |
| 352 | +\newcommand{\crpspilotmrptsmallHonefive}{0.4763} | |
| 353 | +\newcommand{\covfiftypilotmrptsmallHonefive}{55} | |
| 354 | +\newcommand{\covninetyfivepilotmrptsmallHonefive}{95.9} | |
| 355 | +\newcommand{\crpspilotmrptsmallHthreezero}{0.4831} | |
| 356 | +\newcommand{\covfiftypilotmrptsmallHthreezero}{53} | |
| 357 | +\newcommand{\covninetyfivepilotmrptsmallHthreezero}{95.2} | |
| 358 | +\newcommand{\crpspilotmrptsmallHsixzero}{0.4736} | |
| 359 | +\newcommand{\covfiftypilotmrptsmallHsixzero}{54} | |
| 360 | +\newcommand{\covninetyfivepilotmrptsmallHsixzero}{94.7} | |
| 361 | +\newcommand{\crpspilotnaiverwHfive}{0.4803} | |
| 362 | +\newcommand{\covfiftypilotnaiverwHfive}{62} | |
| 363 | +\newcommand{\covninetyfivepilotnaiverwHfive}{96.5} | |
| 364 | +\newcommand{\crpspilotnaiverwHonefive}{0.4874} | |
| 365 | +\newcommand{\covfiftypilotnaiverwHonefive}{61} | |
| 366 | +\newcommand{\covninetyfivepilotnaiverwHonefive}{96.4} | |
| 367 | +\newcommand{\crpspilotnaiverwHthreezero}{0.4952} | |
| 368 | +\newcommand{\covfiftypilotnaiverwHthreezero}{60} | |
| 369 | +\newcommand{\covninetyfivepilotnaiverwHthreezero}{96.2} | |
| 370 | +\newcommand{\crpspilotnaiverwHsixzero}{0.4819} | |
| 371 | +\newcommand{\covfiftypilotnaiverwHsixzero}{61} | |
| 372 | +\newcommand{\covninetyfivepilotnaiverwHsixzero}{96.9} | |
| 373 | +\newcommand{\crpspilotridgeHfive}{0.4734} | |
| 374 | +\newcommand{\covfiftypilotridgeHfive}{41} | |
| 375 | +\newcommand{\covninetyfivepilotridgeHfive}{91.1} | |
| 376 | +\newcommand{\crpspilotridgeHonefive}{0.4765} | |
| 377 | +\newcommand{\covfiftypilotridgeHonefive}{44} | |
| 378 | +\newcommand{\covninetyfivepilotridgeHonefive}{93.9} | |
| 379 | +\newcommand{\crpspilotridgeHthreezero}{0.4842} | |
| 380 | +\newcommand{\covfiftypilotridgeHthreezero}{44} | |
| 381 | +\newcommand{\covninetyfivepilotridgeHthreezero}{93.9} | |
| 382 | +\newcommand{\crpspilotridgeHsixzero}{0.4723} | |
| 383 | +\newcommand{\covfiftypilotridgeHsixzero}{46} | |
| 384 | +\newcommand{\covninetyfivepilotridgeHsixzero}{93.9} | |
| 385 | +\newcommand{\crpspilotseasonalvolHfive}{0.4746} | |
| 386 | +\newcommand{\covfiftypilotseasonalvolHfive}{53} | |
| 387 | +\newcommand{\covninetyfivepilotseasonalvolHfive}{93.7} | |
| 388 | +\newcommand{\crpspilotseasonalvolHonefive}{0.4793} | |
| 389 | +\newcommand{\covfiftypilotseasonalvolHonefive}{53} | |
| 390 | +\newcommand{\covninetyfivepilotseasonalvolHonefive}{93.6} | |
| 391 | +\newcommand{\crpspilotseasonalvolHthreezero}{0.4870} | |
| 392 | +\newcommand{\covfiftypilotseasonalvolHthreezero}{52} | |
| 393 | +\newcommand{\covninetyfivepilotseasonalvolHthreezero}{93.2} | |
| 394 | +\newcommand{\crpspilotseasonalvolHsixzero}{0.4767} | |
| 395 | +\newcommand{\covfiftypilotseasonalvolHsixzero}{52} | |
| 396 | +\newcommand{\covninetyfivepilotseasonalvolHsixzero}{92.6} | |
| 397 | +\newcommand{\crpspilottcnHfive}{0.4687} | |
| 398 | +\newcommand{\covfiftypilottcnHfive}{54} | |
| 399 | +\newcommand{\covninetyfivepilottcnHfive}{95.9} | |
| 400 | +\newcommand{\crpspilottcnHonefive}{0.4767} | |
| 401 | +\newcommand{\covfiftypilottcnHonefive}{55} | |
| 402 | +\newcommand{\covninetyfivepilottcnHonefive}{95.5} | |
| 403 | +\newcommand{\crpspilottcnHthreezero}{0.4838} | |
| 404 | +\newcommand{\covfiftypilottcnHthreezero}{52} | |
| 405 | +\newcommand{\covninetyfivepilottcnHthreezero}{95.0} | |
| 406 | +\newcommand{\crpspilottcnHsixzero}{0.4743} | |
| 407 | +\newcommand{\covfiftypilottcnHsixzero}{54} | |
| 408 | +\newcommand{\covninetyfivepilottcnHsixzero}{94.6} | |
| 409 | +\newcommand{\relmainelasticnetcrpsHfive}{-2.88} | |
| 410 | +\newcommand{\dmrelmainelasticnetcrpsHfive}{-33.2} | |
| 411 | +\newcommand{\relmainelasticnetcrpsHonefive}{-4.35} | |
| 412 | +\newcommand{\dmrelmainelasticnetcrpsHonefive}{-58.2} | |
| 413 | +\newcommand{\relmainelasticnetcrpsHthreezero}{-4.56} | |
| 414 | +\newcommand{\dmrelmainelasticnetcrpsHthreezero}{-46.1} | |
| 415 | +\newcommand{\relmainelasticnetcrpsHsixzero}{-4.89} | |
| 416 | +\newcommand{\dmrelmainelasticnetcrpsHsixzero}{-36.2} | |
| 417 | +\newcommand{\relmainewmacrpsHfive}{-3.65} | |
| 418 | +\newcommand{\dmrelmainewmacrpsHfive}{-57.2} | |
| 419 | +\newcommand{\relmainewmacrpsHonefive}{-3.69} | |
| 420 | +\newcommand{\dmrelmainewmacrpsHonefive}{-53.4} | |
| 421 | +\newcommand{\relmainewmacrpsHthreezero}{-3.60} | |
| 422 | +\newcommand{\dmrelmainewmacrpsHthreezero}{-37.3} | |
| 423 | +\newcommand{\relmainewmacrpsHsixzero}{-3.47} | |
| 424 | +\newcommand{\dmrelmainewmacrpsHsixzero}{-25.5} | |
| 425 | +\newcommand{\relmaingarchtcrpsHfive}{-3.60} | |
| 426 | +\newcommand{\dmrelmaingarchtcrpsHfive}{-57.1} | |
| 427 | +\newcommand{\relmaingarchtcrpsHonefive}{-3.77} | |
| 428 | +\newcommand{\dmrelmaingarchtcrpsHonefive}{-56.0} | |
| 429 | +\newcommand{\relmaingarchtcrpsHthreezero}{-3.70} | |
| 430 | +\newcommand{\dmrelmaingarchtcrpsHthreezero}{-40.5} | |
| 431 | +\newcommand{\relmaingarchtcrpsHsixzero}{-3.40} | |
| 432 | +\newcommand{\dmrelmaingarchtcrpsHsixzero}{-27.9} | |
| 433 | +\newcommand{\relmainharrvcrpsHfive}{-2.19} | |
| 434 | +\newcommand{\dmrelmainharrvcrpsHfive}{-35.7} | |
| 435 | +\newcommand{\relmainharrvcrpsHonefive}{-4.36} | |
| 436 | +\newcommand{\dmrelmainharrvcrpsHonefive}{-64.1} | |
| 437 | +\newcommand{\relmainharrvcrpsHthreezero}{-4.56} | |
| 438 | +\newcommand{\dmrelmainharrvcrpsHthreezero}{-47.4} | |
| 439 | +\newcommand{\relmainharrvcrpsHsixzero}{-4.89} | |
| 440 | +\newcommand{\dmrelmainharrvcrpsHsixzero}{-36.6} | |
| 441 | +\newcommand{\relmainlightgbmcrpsHfive}{-2.88} | |
| 442 | +\newcommand{\dmrelmainlightgbmcrpsHfive}{-33.4} | |
| 443 | +\newcommand{\relmainlightgbmcrpsHonefive}{-4.12} | |
| 444 | +\newcommand{\dmrelmainlightgbmcrpsHonefive}{-51.1} | |
| 445 | +\newcommand{\relmainlightgbmcrpsHthreezero}{-4.56} | |
| 446 | +\newcommand{\dmrelmainlightgbmcrpsHthreezero}{-47.4} | |
| 447 | +\newcommand{\relmainlightgbmcrpsHsixzero}{-4.85} | |
| 448 | +\newcommand{\dmrelmainlightgbmcrpsHsixzero}{-37.6} | |
| 449 | +\newcommand{\relmainmlpcrpsHfive}{-3.94} | |
| 450 | +\newcommand{\dmrelmainmlpcrpsHfive}{-71.6} | |
| 451 | +\newcommand{\relmainmlpcrpsHonefive}{-3.93} | |
| 452 | +\newcommand{\dmrelmainmlpcrpsHonefive}{-68.6} | |
| 453 | +\newcommand{\relmainmlpcrpsHthreezero}{-3.94} | |
| 454 | +\newcommand{\dmrelmainmlpcrpsHthreezero}{-51.5} | |
| 455 | +\newcommand{\relmainmlpcrpsHsixzero}{-4.07} | |
| 456 | +\newcommand{\dmrelmainmlpcrpsHsixzero}{-38.7} | |
| 457 | +\newcommand{\relmainmrptbasecrpsHfive}{-4.04} | |
| 458 | +\newcommand{\dmrelmainmrptbasecrpsHfive}{-69.5} | |
| 459 | +\newcommand{\relmainmrptbasecrpsHonefive}{-4.04} | |
| 460 | +\newcommand{\dmrelmainmrptbasecrpsHonefive}{-67.2} | |
| 461 | +\newcommand{\relmainmrptbasecrpsHthreezero}{-4.06} | |
| 462 | +\newcommand{\dmrelmainmrptbasecrpsHthreezero}{-51.3} | |
| 463 | +\newcommand{\relmainmrptbasecrpsHsixzero}{-4.23} | |
| 464 | +\newcommand{\dmrelmainmrptbasecrpsHsixzero}{-39.8} | |
| 465 | +\newcommand{\relmainmrptsmallonemonlycrpsHfive}{-4.02} | |
| 466 | +\newcommand{\dmrelmainmrptsmallonemonlycrpsHfive}{-69.2} | |
| 467 | +\newcommand{\relmainmrptsmallonemonlycrpsHonefive}{-4.00} | |
| 468 | +\newcommand{\dmrelmainmrptsmallonemonlycrpsHonefive}{-66.9} | |
| 469 | +\newcommand{\relmainmrptsmallonemonlycrpsHthreezero}{-4.00} | |
| 470 | +\newcommand{\dmrelmainmrptsmallonemonlycrpsHthreezero}{-50.4} | |
| 471 | +\newcommand{\relmainmrptsmallonemonlycrpsHsixzero}{-4.17} | |
| 472 | +\newcommand{\dmrelmainmrptsmallonemonlycrpsHsixzero}{-39.6} | |
| 473 | +\newcommand{\relmainmrptsmallcrpsHfive}{-4.05} | |
| 474 | +\newcommand{\dmrelmainmrptsmallcrpsHfive}{-69.3} | |
| 475 | +\newcommand{\relmainmrptsmallcrpsHonefive}{-4.03} | |
| 476 | +\newcommand{\dmrelmainmrptsmallcrpsHonefive}{-67.0} | |
| 477 | +\newcommand{\relmainmrptsmallcrpsHthreezero}{-4.05} | |
| 478 | +\newcommand{\dmrelmainmrptsmallcrpsHthreezero}{-50.6} | |
| 479 | +\newcommand{\relmainmrptsmallcrpsHsixzero}{-4.27} | |
| 480 | +\newcommand{\dmrelmainmrptsmallcrpsHsixzero}{-39.7} | |
| 481 | +\newcommand{\relmainridgecrpsHfive}{-2.88} | |
| 482 | +\newcommand{\dmrelmainridgecrpsHfive}{-33.2} | |
| 483 | +\newcommand{\relmainridgecrpsHonefive}{-4.35} | |
| 484 | +\newcommand{\dmrelmainridgecrpsHonefive}{-58.3} | |
| 485 | +\newcommand{\relmainridgecrpsHthreezero}{-4.55} | |
| 486 | +\newcommand{\dmrelmainridgecrpsHthreezero}{-45.9} | |
| 487 | +\newcommand{\relmainridgecrpsHsixzero}{-4.89} | |
| 488 | +\newcommand{\dmrelmainridgecrpsHsixzero}{-36.2} | |
| 489 | +\newcommand{\relmainseasonalvolcrpsHfive}{-2.89} | |
| 490 | +\newcommand{\dmrelmainseasonalvolcrpsHfive}{-48.8} | |
| 491 | +\newcommand{\relmainseasonalvolcrpsHonefive}{-3.09} | |
| 492 | +\newcommand{\dmrelmainseasonalvolcrpsHonefive}{-49.9} | |
| 493 | +\newcommand{\relmainseasonalvolcrpsHthreezero}{-3.22} | |
| 494 | +\newcommand{\dmrelmainseasonalvolcrpsHthreezero}{-39.3} | |
| 495 | +\newcommand{\relmainseasonalvolcrpsHsixzero}{-3.44} | |
| 496 | +\newcommand{\dmrelmainseasonalvolcrpsHsixzero}{-30.7} | |
| 497 | +\newcommand{\relmaintcncrpsHfive}{-3.93} | |
| 498 | +\newcommand{\dmrelmaintcncrpsHfive}{-69.2} | |
| 499 | +\newcommand{\relmaintcncrpsHonefive}{-3.75} | |
| 500 | +\newcommand{\dmrelmaintcncrpsHonefive}{-65.1} | |
| 501 | +\newcommand{\relmaintcncrpsHthreezero}{-3.68} | |
| 502 | +\newcommand{\dmrelmaintcncrpsHthreezero}{-48.7} | |
| 503 | +\newcommand{\relmaintcncrpsHsixzero}{-3.73} | |
| 504 | +\newcommand{\dmrelmaintcncrpsHsixzero}{-37.3} | |
| 505 | +\newcommand{\relmainelasticnetwisHfive}{-2.83} | |
| 506 | +\newcommand{\dmrelmainelasticnetwisHfive}{-29.8} | |
| 507 | +\newcommand{\relmainelasticnetwisHonefive}{-4.49} | |
| 508 | +\newcommand{\dmrelmainelasticnetwisHonefive}{-56.5} | |
| 509 | +\newcommand{\relmainelasticnetwisHthreezero}{-4.69} | |
| 510 | +\newcommand{\dmrelmainelasticnetwisHthreezero}{-44.9} | |
| 511 | +\newcommand{\relmainelasticnetwisHsixzero}{-5.02} | |
| 512 | +\newcommand{\dmrelmainelasticnetwisHsixzero}{-35.0} | |
| 513 | +\newcommand{\relmainewmawisHfive}{-3.75} | |
| 514 | +\newcommand{\dmrelmainewmawisHfive}{-54.5} | |
| 515 | +\newcommand{\relmainewmawisHonefive}{-3.75} | |
| 516 | +\newcommand{\dmrelmainewmawisHonefive}{-50.4} | |
| 517 | +\newcommand{\relmainewmawisHthreezero}{-3.60} | |
| 518 | +\newcommand{\dmrelmainewmawisHthreezero}{-34.8} | |
| 519 | +\newcommand{\relmainewmawisHsixzero}{-3.40} | |
| 520 | +\newcommand{\dmrelmainewmawisHsixzero}{-23.3} | |
| 521 | +\newcommand{\relmaingarchtwisHfive}{-3.66} | |
| 522 | +\newcommand{\dmrelmaingarchtwisHfive}{-54.1} | |
| 523 | +\newcommand{\relmaingarchtwisHonefive}{-3.79} | |
| 524 | +\newcommand{\dmrelmaingarchtwisHonefive}{-52.8} | |
| 525 | +\newcommand{\relmaingarchtwisHthreezero}{-3.67} | |
| 526 | +\newcommand{\dmrelmaingarchtwisHthreezero}{-37.7} | |
| 527 | +\newcommand{\relmaingarchtwisHsixzero}{-3.29} | |
| 528 | +\newcommand{\dmrelmaingarchtwisHsixzero}{-25.3} | |
| 529 | +\newcommand{\relmainharrvwisHfive}{-2.00} | |
| 530 | +\newcommand{\dmrelmainharrvwisHfive}{-29.7} | |
| 531 | +\newcommand{\relmainharrvwisHonefive}{-4.49} | |
| 532 | +\newcommand{\dmrelmainharrvwisHonefive}{-62.7} | |
| 533 | +\newcommand{\relmainharrvwisHthreezero}{-4.67} | |
| 534 | +\newcommand{\dmrelmainharrvwisHthreezero}{-46.4} | |
| 535 | +\newcommand{\relmainharrvwisHsixzero}{-4.99} | |
| 536 | +\newcommand{\dmrelmainharrvwisHsixzero}{-35.5} | |
| 537 | +\newcommand{\relmainlightgbmwisHfive}{-2.79} | |
| 538 | +\newcommand{\dmrelmainlightgbmwisHfive}{-30.1} | |
| 539 | +\newcommand{\relmainlightgbmwisHonefive}{-4.26} | |
| 540 | +\newcommand{\dmrelmainlightgbmwisHonefive}{-50.5} | |
| 541 | +\newcommand{\relmainlightgbmwisHthreezero}{-4.72} | |
| 542 | +\newcommand{\dmrelmainlightgbmwisHthreezero}{-46.8} | |
| 543 | +\newcommand{\relmainlightgbmwisHsixzero}{-5.01} | |
| 544 | +\newcommand{\dmrelmainlightgbmwisHsixzero}{-36.9} | |
| 545 | +\newcommand{\relmainmlpwisHfive}{-4.17} | |
| 546 | +\newcommand{\dmrelmainmlpwisHfive}{-71.5} | |
| 547 | +\newcommand{\relmainmlpwisHonefive}{-4.15} | |
| 548 | +\newcommand{\dmrelmainmlpwisHonefive}{-68.5} | |
| 549 | +\newcommand{\relmainmlpwisHthreezero}{-4.15} | |
| 550 | +\newcommand{\dmrelmainmlpwisHthreezero}{-51.3} | |
| 551 | +\newcommand{\relmainmlpwisHsixzero}{-4.28} | |
| 552 | +\newcommand{\dmrelmainmlpwisHsixzero}{-38.1} | |
| 553 | +\newcommand{\relmainmrptbasewisHfive}{-4.28} | |
| 554 | +\newcommand{\dmrelmainmrptbasewisHfive}{-68.8} | |
| 555 | +\newcommand{\relmainmrptbasewisHonefive}{-4.28} | |
| 556 | +\newcommand{\dmrelmainmrptbasewisHonefive}{-66.7} | |
| 557 | +\newcommand{\relmainmrptbasewisHthreezero}{-4.29} | |
| 558 | +\newcommand{\dmrelmainmrptbasewisHthreezero}{-51.0} | |
| 559 | +\newcommand{\relmainmrptbasewisHsixzero}{-4.44} | |
| 560 | +\newcommand{\dmrelmainmrptbasewisHsixzero}{-39.3} | |
| 561 | +\newcommand{\relmainmrptsmallonemonlywisHfive}{-4.26} | |
| 562 | +\newcommand{\dmrelmainmrptsmallonemonlywisHfive}{-68.4} | |
| 563 | +\newcommand{\relmainmrptsmallonemonlywisHonefive}{-4.23} | |
| 564 | +\newcommand{\dmrelmainmrptsmallonemonlywisHonefive}{-66.3} | |
| 565 | +\newcommand{\relmainmrptsmallonemonlywisHthreezero}{-4.22} | |
| 566 | +\newcommand{\dmrelmainmrptsmallonemonlywisHthreezero}{-50.0} | |
| 567 | +\newcommand{\relmainmrptsmallonemonlywisHsixzero}{-4.38} | |
| 568 | +\newcommand{\dmrelmainmrptsmallonemonlywisHsixzero}{-38.8} | |
| 569 | +\newcommand{\relmainmrptsmallwisHfive}{-4.30} | |
| 570 | +\newcommand{\dmrelmainmrptsmallwisHfive}{-68.4} | |
| 571 | +\newcommand{\relmainmrptsmallwisHonefive}{-4.28} | |
| 572 | +\newcommand{\dmrelmainmrptsmallwisHonefive}{-66.6} | |
| 573 | +\newcommand{\relmainmrptsmallwisHthreezero}{-4.28} | |
| 574 | +\newcommand{\dmrelmainmrptsmallwisHthreezero}{-50.4} | |
| 575 | +\newcommand{\relmainmrptsmallwisHsixzero}{-4.50} | |
| 576 | +\newcommand{\dmrelmainmrptsmallwisHsixzero}{-39.2} | |
| 577 | +\newcommand{\relmainridgewisHfive}{-2.83} | |
| 578 | +\newcommand{\dmrelmainridgewisHfive}{-29.9} | |
| 579 | +\newcommand{\relmainridgewisHonefive}{-4.50} | |
| 580 | +\newcommand{\dmrelmainridgewisHonefive}{-56.7} | |
| 581 | +\newcommand{\relmainridgewisHthreezero}{-4.68} | |
| 582 | +\newcommand{\dmrelmainridgewisHthreezero}{-44.7} | |
| 583 | +\newcommand{\relmainridgewisHsixzero}{-5.02} | |
| 584 | +\newcommand{\dmrelmainridgewisHsixzero}{-35.0} | |
| 585 | +\newcommand{\relmainseasonalvolwisHfive}{-3.00} | |
| 586 | +\newcommand{\dmrelmainseasonalvolwisHfive}{-46.4} | |
| 587 | +\newcommand{\relmainseasonalvolwisHonefive}{-3.20} | |
| 588 | +\newcommand{\dmrelmainseasonalvolwisHonefive}{-47.8} | |
| 589 | +\newcommand{\relmainseasonalvolwisHthreezero}{-3.33} | |
| 590 | +\newcommand{\dmrelmainseasonalvolwisHthreezero}{-37.8} | |
| 591 | +\newcommand{\relmainseasonalvolwisHsixzero}{-3.54} | |
| 592 | +\newcommand{\dmrelmainseasonalvolwisHsixzero}{-29.1} | |
| 593 | +\newcommand{\relmaintcnwisHfive}{-4.16} | |
| 594 | +\newcommand{\dmrelmaintcnwisHfive}{-68.4} | |
| 595 | +\newcommand{\relmaintcnwisHonefive}{-3.96} | |
| 596 | +\newcommand{\dmrelmaintcnwisHonefive}{-64.5} | |
| 597 | +\newcommand{\relmaintcnwisHthreezero}{-3.88} | |
| 598 | +\newcommand{\dmrelmaintcnwisHthreezero}{-48.4} | |
| 599 | +\newcommand{\relmaintcnwisHsixzero}{-3.92} | |
| 600 | +\newcommand{\dmrelmaintcnwisHsixzero}{-36.8} | |
| 601 | +\newcommand{\relmainelasticnetqlikeHfive}{+5514663565784.96} | |
| 602 | +\newcommand{\dmrelmainelasticnetqlikeHfive}{7.5} | |
| 603 | +\newcommand{\relmainelasticnetqlikeHonefive}{-12129129818422.78} | |
| 604 | +\newcommand{\dmrelmainelasticnetqlikeHonefive}{-21.2} | |
| 605 | +\newcommand{\relmainelasticnetqlikeHthreezero}{-12468574596082.83} | |
| 606 | +\newcommand{\dmrelmainelasticnetqlikeHthreezero}{-20.4} | |
| 607 | +\newcommand{\relmainelasticnetqlikeHsixzero}{-12234566499031.67} | |
| 608 | +\newcommand{\dmrelmainelasticnetqlikeHsixzero}{-17.2} | |
| 609 | +\newcommand{\relmainewmaqlikeHfive}{-12797135612615.71} | |
| 610 | +\newcommand{\dmrelmainewmaqlikeHfive}{-41.9} | |
| 611 | +\newcommand{\relmainewmaqlikeHonefive}{-10996225269347.05} | |
| 612 | +\newcommand{\dmrelmainewmaqlikeHonefive}{-30.9} | |
| 613 | +\newcommand{\relmainewmaqlikeHthreezero}{-8956891977333.71} | |
| 614 | +\newcommand{\dmrelmainewmaqlikeHthreezero}{-18.6} | |
| 615 | +\newcommand{\relmainewmaqlikeHsixzero}{-6156613654049.44} | |
| 616 | +\newcommand{\dmrelmainewmaqlikeHsixzero}{-9.7} | |
| 617 | +\newcommand{\relmaingarchtqlikeHfive}{-3792274777371.91} | |
| 618 | +\newcommand{\dmrelmaingarchtqlikeHfive}{-4.2} | |
| 619 | +\newcommand{\relmaingarchtqlikeHonefive}{-2936683613506.50} | |
| 620 | +\newcommand{\dmrelmaingarchtqlikeHonefive}{-4.8} | |
| 621 | +\newcommand{\relmaingarchtqlikeHthreezero}{-1014981889598.51} | |
| 622 | +\newcommand{\dmrelmaingarchtqlikeHthreezero}{-1.7} | |
| 623 | +\newcommand{\relmaingarchtqlikeHsixzero}{+2553431567866.42} | |
| 624 | +\newcommand{\dmrelmaingarchtqlikeHsixzero}{4.3} | |
| 625 | +\newcommand{\relmainharrvqlikeHfive}{+1922904424583.55} | |
| 626 | +\newcommand{\dmrelmainharrvqlikeHfive}{4.0} | |
| 627 | +\newcommand{\relmainharrvqlikeHonefive}{-11677912373599.43} | |
| 628 | +\newcommand{\dmrelmainharrvqlikeHonefive}{-9.2} | |
| 629 | +\newcommand{\relmainharrvqlikeHthreezero}{-11280891155603.60} | |
| 630 | +\newcommand{\dmrelmainharrvqlikeHthreezero}{-11.2} | |
| 631 | +\newcommand{\relmainharrvqlikeHsixzero}{-11508236846123.03} | |
| 632 | +\newcommand{\dmrelmainharrvqlikeHsixzero}{-17.7} | |
| 633 | +\newcommand{\relmainlightgbmqlikeHfive}{+1814267205302873.75} | |
| 634 | +\newcommand{\dmrelmainlightgbmqlikeHfive}{4.8} | |
| 635 | +\newcommand{\relmainlightgbmqlikeHonefive}{+11471871421175.42} | |
| 636 | +\newcommand{\dmrelmainlightgbmqlikeHonefive}{0.8} | |
| 637 | +\newcommand{\relmainlightgbmqlikeHthreezero}{-13278787159454.87} | |
| 638 | +\newcommand{\dmrelmainlightgbmqlikeHthreezero}{-25.8} | |
| 639 | +\newcommand{\relmainlightgbmqlikeHsixzero}{-13466213447329.12} | |
| 640 | +\newcommand{\dmrelmainlightgbmqlikeHsixzero}{-26.1} | |
| 641 | +\newcommand{\relmainmlpqlikeHfive}{-15818212313424.51} | |
| 642 | +\newcommand{\dmrelmainmlpqlikeHfive}{-41.8} | |
| 643 | +\newcommand{\relmainmlpqlikeHonefive}{-14508869311135.06} | |
| 644 | +\newcommand{\dmrelmainmlpqlikeHonefive}{-36.7} | |
| 645 | +\newcommand{\relmainmlpqlikeHthreezero}{-13489944655719.03} | |
| 646 | +\newcommand{\dmrelmainmlpqlikeHthreezero}{-28.8} | |
| 647 | +\newcommand{\relmainmlpqlikeHsixzero}{-12445594328523.75} | |
| 648 | +\newcommand{\dmrelmainmlpqlikeHsixzero}{-19.9} | |
| 649 | +\newcommand{\relmainmrptbaseqlikeHfive}{-17153971110963.66} | |
| 650 | +\newcommand{\dmrelmainmrptbaseqlikeHfive}{-60.7} | |
| 651 | +\newcommand{\relmainmrptbaseqlikeHonefive}{-16037277205437.76} | |
| 652 | +\newcommand{\dmrelmainmrptbaseqlikeHonefive}{-48.1} | |
| 653 | +\newcommand{\relmainmrptbaseqlikeHthreezero}{-15081771195336.03} | |
| 654 | +\newcommand{\dmrelmainmrptbaseqlikeHthreezero}{-37.9} | |
| 655 | +\newcommand{\relmainmrptbaseqlikeHsixzero}{-14340084012486.90} | |
| 656 | +\newcommand{\dmrelmainmrptbaseqlikeHsixzero}{-30.2} | |
| 657 | +\newcommand{\relmainmrptsmallonemonlyqlikeHfive}{-17184931027568.06} | |
| 658 | +\newcommand{\dmrelmainmrptsmallonemonlyqlikeHfive}{-60.5} | |
| 659 | +\newcommand{\relmainmrptsmallonemonlyqlikeHonefive}{-15902869282831.41} | |
| 660 | +\newcommand{\dmrelmainmrptsmallonemonlyqlikeHonefive}{-45.2} | |
| 661 | +\newcommand{\relmainmrptsmallonemonlyqlikeHthreezero}{-14857414727344.76} | |
| 662 | +\newcommand{\dmrelmainmrptsmallonemonlyqlikeHthreezero}{-34.7} | |
| 663 | +\newcommand{\relmainmrptsmallonemonlyqlikeHsixzero}{-14011901777049.01} | |
| 664 | +\newcommand{\dmrelmainmrptsmallonemonlyqlikeHsixzero}{-28.0} | |
| 665 | +\newcommand{\relmainmrptsmallqlikeHfive}{-17518582839370.88} | |
| 666 | +\newcommand{\dmrelmainmrptsmallqlikeHfive}{-61.1} | |
| 667 | +\newcommand{\relmainmrptsmallqlikeHonefive}{-16395858212306.31} | |
| 668 | +\newcommand{\dmrelmainmrptsmallqlikeHonefive}{-59.2} | |
| 669 | +\newcommand{\relmainmrptsmallqlikeHthreezero}{-15469510096077.54} | |
| 670 | +\newcommand{\dmrelmainmrptsmallqlikeHthreezero}{-47.9} | |
| 671 | +\newcommand{\relmainmrptsmallqlikeHsixzero}{-14813941021870.59} | |
| 672 | +\newcommand{\dmrelmainmrptsmallqlikeHsixzero}{-38.0} | |
| 673 | +\newcommand{\relmainridgeqlikeHfive}{+5434479946610.18} | |
| 674 | +\newcommand{\dmrelmainridgeqlikeHfive}{7.4} | |
| 675 | +\newcommand{\relmainridgeqlikeHonefive}{-12177565285940.69} | |
| 676 | +\newcommand{\dmrelmainridgeqlikeHonefive}{-21.4} | |
| 677 | +\newcommand{\relmainridgeqlikeHthreezero}{-12517051234684.73} | |
| 678 | +\newcommand{\dmrelmainridgeqlikeHthreezero}{-20.7} | |
| 679 | +\newcommand{\relmainridgeqlikeHsixzero}{-12281264246708.48} | |
| 680 | +\newcommand{\dmrelmainridgeqlikeHsixzero}{-17.5} | |
| 681 | +\newcommand{\relmainseasonalvolqlikeHfive}{-8472593190631.71} | |
| 682 | +\newcommand{\dmrelmainseasonalvolqlikeHfive}{-26.5} | |
| 683 | +\newcommand{\relmainseasonalvolqlikeHonefive}{-8305269577503.39} | |
| 684 | +\newcommand{\dmrelmainseasonalvolqlikeHonefive}{-23.8} | |
| 685 | +\newcommand{\relmainseasonalvolqlikeHthreezero}{-7325382995932.99} | |
| 686 | +\newcommand{\dmrelmainseasonalvolqlikeHthreezero}{-14.1} | |
| 687 | +\newcommand{\relmainseasonalvolqlikeHsixzero}{-6019653909459.67} | |
| 688 | +\newcommand{\dmrelmainseasonalvolqlikeHsixzero}{-7.4} | |
| 689 | +\newcommand{\relmaintcnqlikeHfive}{-16924042856514.05} | |
| 690 | +\newcommand{\dmrelmaintcnqlikeHfive}{-63.3} | |
| 691 | +\newcommand{\relmaintcnqlikeHonefive}{-15020597397889.10} | |
| 692 | +\newcommand{\dmrelmaintcnqlikeHonefive}{-35.3} | |
| 693 | +\newcommand{\relmaintcnqlikeHthreezero}{-13794157215647.81} | |
| 694 | +\newcommand{\dmrelmaintcnqlikeHthreezero}{-23.8} | |
| 695 | +\newcommand{\relmaintcnqlikeHsixzero}{-13055303736382.31} | |
| 696 | +\newcommand{\dmrelmaintcnqlikeHsixzero}{-25.8} | |
| 697 | +\newcommand{\crpsmainelasticnetHfive}{0.4603} | |
| 698 | +\newcommand{\covfiftymainelasticnetHfive}{37} | |
| 699 | +\newcommand{\covninetyfivemainelasticnetHfive}{89.6} | |
| 700 | +\newcommand{\crpsmainelasticnetHonefive}{0.4406} | |
| 701 | +\newcommand{\covfiftymainelasticnetHonefive}{47} | |
| 702 | +\newcommand{\covninetyfivemainelasticnetHonefive}{94.6} | |
| 703 | +\newcommand{\crpsmainelasticnetHthreezero}{0.4296} | |
| 704 | +\newcommand{\covfiftymainelasticnetHthreezero}{48} | |
| 705 | +\newcommand{\covninetyfivemainelasticnetHthreezero}{95.2} | |
| 706 | +\newcommand{\crpsmainelasticnetHsixzero}{0.4167} | |
| 707 | +\newcommand{\covfiftymainelasticnetHsixzero}{49} | |
| 708 | +\newcommand{\covninetyfivemainelasticnetHsixzero}{95.7} | |
| 709 | +\newcommand{\crpsmainewmaHfive}{0.4547} | |
| 710 | +\newcommand{\covfiftymainewmaHfive}{54} | |
| 711 | +\newcommand{\covninetyfivemainewmaHfive}{96.9} | |
| 712 | +\newcommand{\crpsmainewmaHonefive}{0.4425} | |
| 713 | +\newcommand{\covfiftymainewmaHonefive}{54} | |
| 714 | +\newcommand{\covninetyfivemainewmaHonefive}{97.2} | |
| 715 | +\newcommand{\crpsmainewmaHthreezero}{0.4326} | |
| 716 | +\newcommand{\covfiftymainewmaHthreezero}{55} | |
| 717 | +\newcommand{\covninetyfivemainewmaHthreezero}{97.3} | |
| 718 | +\newcommand{\crpsmainewmaHsixzero}{0.4214} | |
| 719 | +\newcommand{\covfiftymainewmaHsixzero}{56} | |
| 720 | +\newcommand{\covninetyfivemainewmaHsixzero}{97.5} | |
| 721 | +\newcommand{\crpsmaingarchtHfive}{0.4558} | |
| 722 | +\newcommand{\covfiftymaingarchtHfive}{53} | |
| 723 | +\newcommand{\covninetyfivemaingarchtHfive}{96.6} | |
| 724 | +\newcommand{\crpsmaingarchtHonefive}{0.4430} | |
| 725 | +\newcommand{\covfiftymaingarchtHonefive}{55} | |
| 726 | +\newcommand{\covninetyfivemaingarchtHonefive}{97.2} | |
| 727 | +\newcommand{\crpsmaingarchtHthreezero}{0.4333} | |
| 728 | +\newcommand{\covfiftymaingarchtHthreezero}{56} | |
| 729 | +\newcommand{\covninetyfivemaingarchtHthreezero}{97.6} | |
| 730 | +\newcommand{\crpsmaingarchtHsixzero}{0.4232} | |
| 731 | +\newcommand{\covfiftymaingarchtHsixzero}{59} | |
| 732 | +\newcommand{\covninetyfivemaingarchtHsixzero}{97.9} | |
| 733 | +\newcommand{\crpsmainharrvHfive}{0.4615} | |
| 734 | +\newcommand{\covfiftymainharrvHfive}{60} | |
| 735 | +\newcommand{\covninetyfivemainharrvHfive}{98.8} | |
| 736 | +\newcommand{\crpsmainharrvHonefive}{0.4403} | |
| 737 | +\newcommand{\covfiftymainharrvHonefive}{50} | |
| 738 | +\newcommand{\covninetyfivemainharrvHonefive}{96.3} | |
| 739 | +\newcommand{\crpsmainharrvHthreezero}{0.4295} | |
| 740 | +\newcommand{\covfiftymainharrvHthreezero}{48} | |
| 741 | +\newcommand{\covninetyfivemainharrvHthreezero}{96.2} | |
| 742 | +\newcommand{\crpsmainharrvHsixzero}{0.4166} | |
| 743 | +\newcommand{\covfiftymainharrvHsixzero}{49} | |
| 744 | +\newcommand{\covninetyfivemainharrvHsixzero}{96.3} | |
| 745 | +\newcommand{\crpsmainlightgbmHfive}{0.4591} | |
| 746 | +\newcommand{\covfiftymainlightgbmHfive}{38} | |
| 747 | +\newcommand{\covninetyfivemainlightgbmHfive}{90.0} | |
| 748 | +\newcommand{\crpsmainlightgbmHonefive}{0.4415} | |
| 749 | +\newcommand{\covfiftymainlightgbmHonefive}{44} | |
| 750 | +\newcommand{\covninetyfivemainlightgbmHonefive}{94.2} | |
| 751 | +\newcommand{\crpsmainlightgbmHthreezero}{0.4293} | |
| 752 | +\newcommand{\covfiftymainlightgbmHthreezero}{49} | |
| 753 | +\newcommand{\covninetyfivemainlightgbmHthreezero}{95.3} | |
| 754 | +\newcommand{\crpsmainlightgbmHsixzero}{0.4166} | |
| 755 | +\newcommand{\covfiftymainlightgbmHsixzero}{50} | |
| 756 | +\newcommand{\covninetyfivemainlightgbmHsixzero}{95.7} | |
| 757 | +\newcommand{\crpsmainmlpHfive}{0.4538} | |
| 758 | +\newcommand{\covfiftymainmlpHfive}{55} | |
| 759 | +\newcommand{\covninetyfivemainmlpHfive}{95.7} | |
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modified
paper/sections/results.tex
+95 −1
@@ -1 +1,95 @@ | ||
| 1 | −% results — written in P8 | |
| 1 | +\section{Results} | |
| 2 | +\label{sec:results} | |
| 3 | + | |
| 4 | +\subsection{Pilot} | |
| 5 | +The pilot (20 instruments, September--December 2022, test on the last ten sessions, \num{4659} origins) validated | |
| 6 | +the pipeline from export to LaTeX table and gave a first, deliberately unweighted, reading: every volatility-aware | |
| 7 | +model improved on the random walk by 2--3\,\% in CRPS and the multi-resolution MRPT, its one-minute-only variant, a | |
| 8 | +TCN and an MLP were within 0.2\,\% of one another (Table~\ref{tab:pilot_crps_scaled}, Appendix). Nothing was tuned on it. | |
| 9 | + | |
| 10 | +\subsection{Development test (2024): all models beat the random walk, by about four percent} | |
| 11 | +Table~\ref{tab:main_crps_scaled} reports the scaled CRPS of the cumulative return on the \num{986468} evaluation | |
| 12 | +origins of 2024 (240 pooled instruments, 24 origins per session), with trading-day cluster-bootstrap intervals, and | |
| 13 | +Table~\ref{tab:main_compare_crps} the relative change against the random walk with its Diebold--Mariano statistic. | |
| 14 | +Figure~\ref{fig:main_crps} summarises both. Three facts stand out. | |
| 15 | + | |
| 16 | +First, the random walk with a trailing one-minute scale is beaten by every model at every horizon, by | |
| 17 | +3.5--4.9\,\%, with DM statistics between $-25$ and $-72$: minute-level history carries real information about the | |
| 18 | +\emph{dispersion} of the next hour, and the improvement is essentially a volatility improvement (directional | |
| 19 | +accuracy of every location forecast stays at 0.50). | |
| 20 | + | |
| 21 | +Second, the neural family (MRPT-S, MRPT-B, TCN, MLP) is the best at five minutes | |
| 22 | +(scaled CRPS \crpsmainmrptsmallHfive{} for MRPT-S against \crpsmainharrvHfive{} for HAR-RV, a difference of | |
| 23 | +\pwmainmrptsmallvsharrvHfive{}\,\% with $t=\tpwmainmrptsmallvsharrvHfive{}$), whereas the feature-based volatility | |
| 24 | +regressions---HAR-RV, ridge, elastic net and LightGBM---are the best from fifteen minutes on | |
| 25 | +(\crpsmainharrvHsixzero{} against \crpsmainmrptsmallHsixzero{} at sixty minutes; MRPT-S is worse by | |
| 26 | +\pwmainmrptsmallvsharrvHsixzero{}\,\%, $t=\tpwmainmrptsmallvsharrvHsixzero{}$). MRPT-S beats GARCH(1,1)-$t$, EWMA, the TCN | |
| 27 | +and the MLP at every horizon (by 0.1--0.9\,\%, all Holm-adjusted $p<10^{-6}$). | |
| 28 | + | |
| 29 | +Third, and central to the paper, \textbf{Hypothesis~\ref{h1} is rejected in economic terms}: the multi-resolution | |
| 30 | +MRPT-S improves on its one-minute-only twin by \pwmainmrptsmallvsmrptsmallonemonlyHfive{}\,\% at five minutes and | |
| 31 | +\pwmainmrptsmallvsmrptsmallonemonlyHsixzero{}\,\% at sixty minutes. The differences are statistically detectable | |
| 32 | +($t=\tpwmainmrptsmallvsmrptsmallonemonlyHsixzero{}$ at $H=60$, \num{986468} origins over 252 days) but they are an order | |
| 33 | +of magnitude smaller than the gap between any neural model and the random walk, and smaller than the gap between | |
| 34 | +the neural models and HAR-RV at sixty minutes. Five days of 5-minute aggregates and twenty days of 30-minute | |
| 35 | +aggregates add almost nothing that the last 390 one-minute bars do not already contain. Size does not matter | |
| 36 | +either: the 20.7-million-parameter Base model and the 3.5-million-parameter Small model are indistinguishable | |
| 37 | +(\pwmainmrptbasevsmrptsmallHsixzero{}\,\% at $H=60$, Holm $p=\ppwmainmrptbasevsmrptsmallHsixzero{}$). | |
| 38 | + | |
| 39 | + | |
| 40 | +\begin{figure}[htbp]\centering | |
| 41 | +\includegraphics[width=\textwidth]{figures/fig_main_crps.pdf} | |
| 42 | +\caption{Development test 2024 (240 instruments, \num{986468} origins). Panel A: scaled CRPS of the cumulative-return | |
| 43 | +forecast by horizon. Panel B: relative change versus the random walk. Source: \texttt{results/metrics/main/leaderboard\_test.csv}.} | |
| 44 | +\label{fig:main_crps} | |
| 45 | +\end{figure} | |
| 46 | + | |
| 47 | +\begin{figure}[htbp]\centering | |
| 48 | +\includegraphics[width=\textwidth]{figures/fig_main_calibration.pdf} | |
| 49 | +\caption{Empirical coverage of the central 50\,\%, 80\,\% and 95\,\% prediction intervals by horizon (dotted line = nominal), development test 2024.} | |
| 50 | +\label{fig:main_calibration} | |
| 51 | +\end{figure} | |
| 52 | + | |
| 53 | +\begin{figure}[htbp]\centering | |
| 54 | +\includegraphics[width=\textwidth]{figures/fig_main_pit.pdf} | |
| 55 | +\caption{PIT histograms at $H=60$ for the random walk, GARCH(1,1)-$t$, LightGBM and MRPT-S (dashed line = uniform density).} | |
| 56 | +\label{fig:main_pit} | |
| 57 | +\end{figure} | |
| 58 | + | |
| 59 | +\begin{figure}[htbp]\centering | |
| 60 | +\includegraphics[width=\textwidth]{figures/fig_main_training.pdf} | |
| 61 | +\caption{Training (moving average) and validation negative log-likelihood per optimiser step, main study.} | |
| 62 | +\label{fig:main_training} | |
| 63 | +\end{figure} | |
| 64 | + | |
| 65 | +\subsection{Calibration} | |
| 66 | +Table~\ref{tab:main_calibration} and Figure~\ref{fig:main_calibration} show empirical coverage of the 50/80/95\,\% | |
| 67 | +central intervals and the PIT Kolmogorov--Smirnov statistic. The random walk is over-dispersed everywhere (50\,\% | |
| 68 | +intervals cover \covfiftymainnaiverwHsixzero{}\,\% of outcomes at sixty minutes). The Student-$t$ neural models and | |
| 69 | +GARCH/EWMA are nearly nominal at 95\,\% but over-dispersed in the centre (50\,\% coverage 0.55--0.59): their | |
| 70 | +degrees of freedom and scale produce tails that are right and a body that is too wide. HAR-RV, ridge and LightGBM | |
| 71 | +are the best-calibrated models from fifteen minutes on (0.49/0.80/0.96 at sixty minutes, KS 0.008) and the worst at | |
| 72 | +five minutes (50\,\% coverage 0.37, 95\,\% coverage 0.90): a lognormal variance regression on 390-minute features | |
| 73 | +cannot react to the last five minutes. PIT histograms (Figure~\ref{fig:main_pit}) make the same point visually. | |
| 74 | +Scores and calibration thus tell one consistent story: at the shortest horizon the sequence models' ability to | |
| 75 | +read the very last bars wins; at longer horizons a well-specified heterogeneous variance regression with a | |
| 76 | +kurtosis-matched Student-$t$ is both sharper and better calibrated. | |
| 77 | + | |
| 78 | +\subsection{Subgroups} | |
| 79 | +Splitting the MRPT-S versus HAR-RV contrast at sixty minutes by subgroup, HAR-RV's advantage is concentrated in | |
| 80 | +low-dollar-volume stocks ($+1.3$\,\%), low-volatility instruments ($+1.0$\,\%), transport and utilities ($+1.9$\,\%), | |
| 81 | +fixed-income ETFs ($+1.8$\,\%) and the stocks without a SIC code ($+2.8$\,\%); MRPT-S is better on broad-equity, | |
| 82 | +sector and volatility-linked ETFs ($-0.3$ to $-1.1$\,\%) and statistically tied on high-dollar-volume instruments. | |
| 83 | +Afternoon origins favour HAR-RV ($+1.0$\,\%), morning origins much less ($+0.2$\,\%). On stress days (top decile of | |
| 84 | +cross-sectional $\sigma_t$, \num{100846} origins) the ordering is unchanged and every model's coverage moves by at | |
| 85 | +most one percentage point: none of the models breaks under stress, and none gains a special advantage there. | |
| 86 | + | |
| 87 | +\subsection{Economic content (Hypothesis~\ref{h5})} | |
| 88 | +The predictive medians carry no usable directional information. Their correlation with the realised sixty-minute | |
| 89 | +return is 0.003 (MRPT-S), 0.025 (MRPT-B), 0.014 (TCN) and 0.007 (MLP), the typical magnitude of the median is below | |
| 90 | +one basis point, and a sign rule that trades only when the median exceeds an assumed round-trip cost of 1 basis | |
| 91 | +point trades 17\,\% of the origins for a net return of $0.0$ bp $[-1.7, +1.8]$; at 2.5--10 bp the traded share | |
| 92 | +falls below 4\,\% and every interval contains zero. We report this null without further sensitivity analysis. | |
| 93 | + | |
| 94 | +\subsection{Zero-shot transfer and the untouched 2025 period} | |
| 95 | +\IfFileExists{sections/results_heldout.tex}{\input{sections/results_heldout}}{\emph{(Held-out and final-period results are added when the runs complete.)}} | |
added
paper/tables/benchmark.tex
+21 −0
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| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Measured training throughput and memory on the compute node (Apple M3 Ultra{,} m3u96b{,} torch 2.15.0{,} mps; FP32)} | |
| 3 | +\label{tab:benchmark} | |
| 4 | +\begin{tabular}{lrrrrrr} | |
| 5 | +\toprule | |
| 6 | +Preset & Batch & Parameters & Steps/s & Examples/s & Peak memory (MB) & Latency/origin (ms) \\ | |
| 7 | +\midrule | |
| 8 | +small & 32 & 3{,}455{,}619 & 20.81 & 666 & 54 & 0.34 \\ | |
| 9 | +small & 64 & 3{,}455{,}619 & 12.21 & 782 & 69 & 0.25 \\ | |
| 10 | +small & 128 & 3{,}455{,}619 & 5.93 & 758 & 97 & 0.27 \\ | |
| 11 | +spec & 32 & 7{,}677{,}955 & 11.54 & 369 & 114 & 0.59 \\ | |
| 12 | +spec & 64 & 7{,}677{,}955 & 6.29 & 402 & 119 & 0.48 \\ | |
| 13 | +spec & 128 & 7{,}677{,}955 & 2.97 & 380 & 147 & 0.53 \\ | |
| 14 | +base & 32 & 20{,}718{,}339 & 6.11 & 195 & 275 & 5.04 \\ | |
| 15 | +base & 64 & 20{,}718{,}339 & 3.24 & 207 & 284 & 1.59 \\ | |
| 16 | +base & 128 & 20{,}718{,}339 & 1.51 & 193 & 315 & 1.76 \\ | |
| 17 | +\midrule | |
| 18 | +Data loader (64/batch) & 0 workers: 3971 ex/s; 4 workers: 13016 ex/s; 8 workers: 38486 ex/s & & & & & \\ | |
| 19 | +\bottomrule | |
| 20 | +\end{tabular} | |
| 21 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/main_calibration.tex
+24 −0
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| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Main: empirical 50/80/95\% coverage and PIT KS statistic} | |
| 3 | +\label{tab:main_calib} | |
| 4 | +\begin{tabular}{lcccccccccccccccc} | |
| 5 | +\toprule | |
| 6 | +Model & \multicolumn{4}{c}{$H=5$} & \multicolumn{4}{c}{$H=15$} & \multicolumn{4}{c}{$H=30$} & \multicolumn{4}{c}{$H=60$} \\ | |
| 7 | + & 50 & 80 & 95 & KS & 50 & 80 & 95 & KS & 50 & 80 & 95 & KS & 50 & 80 & 95 & KS \\ | |
| 8 | +\midrule | |
| 9 | +Random walk (trailing RMS) & 0.65 & 0.88 & 0.97 & 0.078 & 0.66 & 0.89 & 0.97 & 0.079 & 0.67 & 0.90 & 0.97 & 0.083 & 0.68 & 0.91 & 0.98 & 0.089 \\ | |
| 10 | +Seasonal volatility & 0.56 & 0.82 & 0.94 & 0.031 & 0.56 & 0.83 & 0.94 & 0.031 & 0.56 & 0.83 & 0.95 & 0.033 & 0.57 & 0.83 & 0.95 & 0.034 \\ | |
| 11 | +EWMA-$t$ & 0.54 & 0.83 & 0.97 & 0.023 & 0.54 & 0.84 & 0.97 & 0.024 & 0.55 & 0.85 & 0.97 & 0.028 & 0.56 & 0.86 & 0.97 & 0.034 \\ | |
| 12 | +HAR-RV & 0.60 & 0.89 & 0.99 & 0.058 & 0.50 & 0.81 & 0.96 & 0.008 & 0.48 & 0.80 & 0.96 & 0.009 & 0.49 & 0.80 & 0.96 & 0.008 \\ | |
| 13 | +GARCH(1,1)-$t$ & 0.53 & 0.83 & 0.97 & 0.021 & 0.55 & 0.85 & 0.97 & 0.027 & 0.56 & 0.86 & 0.98 & 0.035 & 0.59 & 0.88 & 0.98 & 0.047 \\ | |
| 14 | +Ridge & 0.37 & 0.67 & 0.90 & 0.076 & 0.47 & 0.77 & 0.95 & 0.018 & 0.48 & 0.78 & 0.95 & 0.015 & 0.49 & 0.80 & 0.96 & 0.009 \\ | |
| 15 | +Elastic net & 0.37 & 0.67 & 0.90 & 0.076 & 0.47 & 0.77 & 0.95 & 0.018 & 0.48 & 0.78 & 0.95 & 0.014 & 0.49 & 0.80 & 0.96 & 0.009 \\ | |
| 16 | +LightGBM & 0.38 & 0.67 & 0.90 & 0.073 & 0.44 & 0.75 & 0.94 & 0.036 & 0.49 & 0.79 & 0.95 & 0.010 & 0.50 & 0.80 & 0.96 & 0.008 \\ | |
| 17 | +MLP (1m) & 0.55 & 0.83 & 0.96 & 0.029 & 0.57 & 0.84 & 0.96 & 0.034 & 0.58 & 0.85 & 0.96 & 0.039 & 0.58 & 0.86 & 0.96 & 0.043 \\ | |
| 18 | +TCN (1m) & 0.56 & 0.84 & 0.96 & 0.032 & 0.57 & 0.85 & 0.96 & 0.037 & 0.58 & 0.85 & 0.96 & 0.042 & 0.59 & 0.86 & 0.96 & 0.046 \\ | |
| 19 | +MRPT-S (1m+5m+30m) & 0.55 & 0.83 & 0.96 & 0.029 & 0.56 & 0.84 & 0.96 & 0.033 & 0.57 & 0.85 & 0.96 & 0.037 & 0.58 & 0.85 & 0.96 & 0.040 \\ | |
| 20 | +MRPT-S (1m only) & 0.55 & 0.83 & 0.96 & 0.030 & 0.56 & 0.84 & 0.96 & 0.033 & 0.57 & 0.85 & 0.96 & 0.037 & 0.58 & 0.85 & 0.96 & 0.041 \\ | |
| 21 | +MRPT-B (1m+5m+30m) & 0.55 & 0.83 & 0.96 & 0.029 & 0.56 & 0.84 & 0.96 & 0.033 & 0.57 & 0.85 & 0.96 & 0.037 & 0.58 & 0.85 & 0.96 & 0.041 \\ | |
| 22 | +\bottomrule | |
| 23 | +\end{tabular} | |
| 24 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/main_compare_crps.tex
+23 −0
@@ -0,0 +1,23 @@ | ||
| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Main: CRPS relative to Random walk (trailing RMS)} | |
| 3 | +\label{tab:main_cmp_crps} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Seasonal volatility & -2.89\% (-48.8) & -3.09\% (-49.9) & -3.22\% (-39.3) & -3.44\% (-30.7) \\ | |
| 9 | +EWMA-$t$ & -3.65\% (-57.2) & -3.69\% (-53.4) & -3.60\% (-37.3) & -3.47\% (-25.5) \\ | |
| 10 | +HAR-RV & -2.19\% (-35.7) & -4.36\% (-64.1) & -4.56\% (-47.4) & -4.89\% (-36.6) \\ | |
| 11 | +GARCH(1,1)-$t$ & -3.60\% (-57.1) & -3.77\% (-56.0) & -3.70\% (-40.5) & -3.40\% (-27.9) \\ | |
| 12 | +Ridge & -2.88\% (-33.2) & -4.35\% (-58.3) & -4.55\% (-45.9) & -4.89\% (-36.2) \\ | |
| 13 | +Elastic net & -2.88\% (-33.2) & -4.35\% (-58.2) & -4.56\% (-46.1) & -4.89\% (-36.2) \\ | |
| 14 | +LightGBM & -2.88\% (-33.4) & -4.12\% (-51.1) & -4.56\% (-47.4) & -4.85\% (-37.6) \\ | |
| 15 | +MLP (1m) & -3.94\% (-71.6) & -3.93\% (-68.6) & -3.94\% (-51.5) & -4.07\% (-38.7) \\ | |
| 16 | +TCN (1m) & -3.93\% (-69.2) & -3.75\% (-65.1) & -3.68\% (-48.7) & -3.73\% (-37.3) \\ | |
| 17 | +MRPT-S (1m+5m+30m) & -4.05\% (-69.3) & -4.03\% (-67.0) & -4.05\% (-50.6) & -4.27\% (-39.7) \\ | |
| 18 | +MRPT-S (1m only) & -4.02\% (-69.2) & -4.00\% (-66.9) & -4.00\% (-50.4) & -4.17\% (-39.6) \\ | |
| 19 | +MRPT-B (1m+5m+30m) & -4.04\% (-69.5) & -4.04\% (-67.2) & -4.06\% (-51.3) & -4.23\% (-39.8) \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| 22 | +\begin{minipage}{0.95\textwidth}\scriptsize Relative change in mean CRPS versus the reference (negative = better); Diebold--Mariano $t$-statistic with HAC variance in parentheses.\end{minipage} | |
| 23 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/main_compare_qlike.tex
+23 −0
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| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Main: QLIKE relative to Random walk (trailing RMS)} | |
| 3 | +\label{tab:main_cmp_qlike} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Seasonal volatility & -8472593190631.71\% (-26.5) & -8305269577503.39\% (-23.8) & -7325382995932.99\% (-14.1) & -6019653909459.67\% (-7.4) \\ | |
| 9 | +EWMA-$t$ & -12797135612615.71\% (-41.9) & -10996225269347.05\% (-30.9) & -8956891977333.71\% (-18.6) & -6156613654049.44\% (-9.7) \\ | |
| 10 | +HAR-RV & +1922904424583.55\% (4.0) & -11677912373599.43\% (-9.2) & -11280891155603.60\% (-11.2) & -11508236846123.03\% (-17.7) \\ | |
| 11 | +GARCH(1,1)-$t$ & -3792274777371.91\% (-4.2) & -2936683613506.50\% (-4.8) & -1014981889598.51\% (-1.7) & +2553431567866.42\% (4.3) \\ | |
| 12 | +Ridge & +5434479946610.18\% (7.4) & -12177565285940.69\% (-21.4) & -12517051234684.73\% (-20.7) & -12281264246708.48\% (-17.5) \\ | |
| 13 | +Elastic net & +5514663565784.96\% (7.5) & -12129129818422.78\% (-21.2) & -12468574596082.83\% (-20.4) & -12234566499031.67\% (-17.2) \\ | |
| 14 | +LightGBM & +1814267205302873.75\% (4.8) & +11471871421175.42\% (0.8) & -13278787159454.87\% (-25.8) & -13466213447329.12\% (-26.1) \\ | |
| 15 | +MLP (1m) & -15818212313424.51\% (-41.8) & -14508869311135.06\% (-36.7) & -13489944655719.03\% (-28.8) & -12445594328523.75\% (-19.9) \\ | |
| 16 | +TCN (1m) & -16924042856514.05\% (-63.3) & -15020597397889.10\% (-35.3) & -13794157215647.81\% (-23.8) & -13055303736382.31\% (-25.8) \\ | |
| 17 | +MRPT-S (1m+5m+30m) & -17518582839370.88\% (-61.1) & -16395858212306.31\% (-59.2) & -15469510096077.54\% (-47.9) & -14813941021870.59\% (-38.0) \\ | |
| 18 | +MRPT-S (1m only) & -17184931027568.06\% (-60.5) & -15902869282831.41\% (-45.2) & -14857414727344.76\% (-34.7) & -14011901777049.01\% (-28.0) \\ | |
| 19 | +MRPT-B (1m+5m+30m) & -17153971110963.66\% (-60.7) & -16037277205437.76\% (-48.1) & -15081771195336.03\% (-37.9) & -14340084012486.90\% (-30.2) \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| 22 | +\begin{minipage}{0.95\textwidth}\scriptsize Relative change in mean QLIKE versus the reference (negative = better); Diebold--Mariano $t$-statistic with HAC variance in parentheses.\end{minipage} | |
| 23 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/main_compare_wis.tex
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| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Main: WIS relative to Random walk (trailing RMS)} | |
| 3 | +\label{tab:main_cmp_wis} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Seasonal volatility & -3.00\% (-46.4) & -3.20\% (-47.8) & -3.33\% (-37.8) & -3.54\% (-29.1) \\ | |
| 9 | +EWMA-$t$ & -3.75\% (-54.5) & -3.75\% (-50.4) & -3.60\% (-34.8) & -3.40\% (-23.3) \\ | |
| 10 | +HAR-RV & -2.00\% (-29.7) & -4.49\% (-62.7) & -4.67\% (-46.4) & -4.99\% (-35.5) \\ | |
| 11 | +GARCH(1,1)-$t$ & -3.66\% (-54.1) & -3.79\% (-52.8) & -3.67\% (-37.7) & -3.29\% (-25.3) \\ | |
| 12 | +Ridge & -2.83\% (-29.9) & -4.50\% (-56.7) & -4.68\% (-44.7) & -5.02\% (-35.0) \\ | |
| 13 | +Elastic net & -2.83\% (-29.8) & -4.49\% (-56.5) & -4.69\% (-44.9) & -5.02\% (-35.0) \\ | |
| 14 | +LightGBM & -2.79\% (-30.1) & -4.26\% (-50.5) & -4.72\% (-46.8) & -5.01\% (-36.9) \\ | |
| 15 | +MLP (1m) & -4.17\% (-71.5) & -4.15\% (-68.5) & -4.15\% (-51.3) & -4.28\% (-38.1) \\ | |
| 16 | +TCN (1m) & -4.16\% (-68.4) & -3.96\% (-64.5) & -3.88\% (-48.4) & -3.92\% (-36.8) \\ | |
| 17 | +MRPT-S (1m+5m+30m) & -4.30\% (-68.4) & -4.28\% (-66.6) & -4.28\% (-50.4) & -4.50\% (-39.2) \\ | |
| 18 | +MRPT-S (1m only) & -4.26\% (-68.4) & -4.23\% (-66.3) & -4.22\% (-50.0) & -4.38\% (-38.8) \\ | |
| 19 | +MRPT-B (1m+5m+30m) & -4.28\% (-68.8) & -4.28\% (-66.7) & -4.29\% (-51.0) & -4.44\% (-39.3) \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| 22 | +\begin{minipage}{0.95\textwidth}\scriptsize Relative change in mean WIS versus the reference (negative = better); Diebold--Mariano $t$-statistic with HAC variance in parentheses.\end{minipage} | |
| 23 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/main_crps_scaled.tex
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| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Main: mean scaled CRPS of the cumulative-return forecast by horizon (minutes)} | |
| 3 | +\label{tab:main_crps_scaled} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Random walk (trailing RMS) & 0.4699 {\scriptsize[0.4648, 0.4754]} & 0.4575 {\scriptsize[0.4515, 0.4639]} & 0.4469 {\scriptsize[0.4412, 0.4538]} & 0.4347 {\scriptsize[0.4271, 0.4441]} \\ | |
| 9 | +Seasonal volatility & 0.4582 {\scriptsize[0.4527, 0.4641]} & 0.4453 {\scriptsize[0.4390, 0.4519]} & 0.4347 {\scriptsize[0.4285, 0.4418]} & 0.4221 {\scriptsize[0.4139, 0.4320]} \\ | |
| 10 | +EWMA-$t$ & 0.4547 {\scriptsize[0.4492, 0.4606]} & 0.4425 {\scriptsize[0.4363, 0.4491]} & 0.4326 {\scriptsize[0.4264, 0.4396]} & 0.4214 {\scriptsize[0.4133, 0.4314]} \\ | |
| 11 | +HAR-RV & 0.4615 {\scriptsize[0.4563, 0.4671]} & 0.4403 {\scriptsize[0.4338, 0.4471]} & 0.4295 {\scriptsize[0.4230, 0.4369]} & 0.4166 {\scriptsize[0.4080, 0.4270]} \\ | |
| 12 | +GARCH(1,1)-$t$ & 0.4558 {\scriptsize[0.4502, 0.4616]} & 0.4430 {\scriptsize[0.4367, 0.4497]} & 0.4333 {\scriptsize[0.4271, 0.4403]} & 0.4232 {\scriptsize[0.4153, 0.4328]} \\ | |
| 13 | +Ridge & 0.4603 {\scriptsize[0.4542, 0.4667]} & 0.4405 {\scriptsize[0.4339, 0.4476]} & 0.4297 {\scriptsize[0.4231, 0.4371]} & 0.4167 {\scriptsize[0.4081, 0.4272]} \\ | |
| 14 | +Elastic net & 0.4603 {\scriptsize[0.4543, 0.4668]} & 0.4406 {\scriptsize[0.4339, 0.4476]} & 0.4296 {\scriptsize[0.4231, 0.4370]} & 0.4167 {\scriptsize[0.4081, 0.4272]} \\ | |
| 15 | +LightGBM & 0.4591 {\scriptsize[0.4531, 0.4655]} & 0.4415 {\scriptsize[0.4347, 0.4484]} & 0.4293 {\scriptsize[0.4228, 0.4366]} & 0.4166 {\scriptsize[0.4080, 0.4269]} \\ | |
| 16 | +MLP (1m) & 0.4538 {\scriptsize[0.4484, 0.4598]} & 0.4421 {\scriptsize[0.4357, 0.4486]} & 0.4319 {\scriptsize[0.4258, 0.4388]} & 0.4197 {\scriptsize[0.4116, 0.4291]} \\ | |
| 17 | +TCN (1m) & 0.4538 {\scriptsize[0.4484, 0.4597]} & 0.4427 {\scriptsize[0.4364, 0.4491]} & 0.4327 {\scriptsize[0.4265, 0.4396]} & 0.4207 {\scriptsize[0.4126, 0.4303]} \\ | |
| 18 | +MRPT-S (1m+5m+30m) & 0.4531 {\scriptsize[0.4476, 0.4590]} & 0.4414 {\scriptsize[0.4351, 0.4479]} & 0.4311 {\scriptsize[0.4249, 0.4381]} & 0.4187 {\scriptsize[0.4105, 0.4284]} \\ | |
| 19 | +MRPT-S (1m only) & 0.4533 {\scriptsize[0.4478, 0.4592]} & 0.4416 {\scriptsize[0.4352, 0.4481]} & 0.4314 {\scriptsize[0.4251, 0.4382]} & 0.4192 {\scriptsize[0.4110, 0.4290]} \\ | |
| 20 | +MRPT-B (1m+5m+30m) & 0.4532 {\scriptsize[0.4478, 0.4591]} & 0.4414 {\scriptsize[0.4351, 0.4479]} & 0.4312 {\scriptsize[0.4249, 0.4381]} & 0.4189 {\scriptsize[0.4107, 0.4287]} \\ | |
| 21 | +\bottomrule | |
| 22 | +\end{tabular} | |
| 23 | +\begin{minipage}{0.95\textwidth}\scriptsize Cluster-bootstrap (trading-day) 95\% intervals in brackets.\end{minipage} | |
| 24 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/main_logscore.tex
+24 −0
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| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Main: mean log score of the cumulative-return forecast by horizon (minutes)} | |
| 3 | +\label{tab:main_logscore} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Random walk (trailing RMS) & nan & nan & nan & nan \\ | |
| 9 | +Seasonal volatility & nan & nan & nan & nan \\ | |
| 10 | +EWMA-$t$ & -5.3800 {\scriptsize[-5.3983, -5.3611]} & -4.8516 {\scriptsize[-4.8704, -4.8300]} & -4.5201 {\scriptsize[-4.5406, -4.4981]} & -4.1899 {\scriptsize[-4.2130, -4.1628]} \\ | |
| 11 | +HAR-RV & -5.3419 {\scriptsize[-5.3591, -5.3235]} & -4.8627 {\scriptsize[-4.8820, -4.8408]} & -4.5354 {\scriptsize[-4.5574, -4.5123]} & -4.2140 {\scriptsize[-4.2385, -4.1858]} \\ | |
| 12 | +GARCH(1,1)-$t$ & -5.3754 {\scriptsize[-5.3940, -5.3561]} & -4.8509 {\scriptsize[-4.8693, -4.8293]} & -4.5188 {\scriptsize[-4.5389, -4.4974]} & -4.1823 {\scriptsize[-4.2040, -4.1573]} \\ | |
| 13 | +Ridge & -5.3260 {\scriptsize[-5.3484, -5.3035]} & -4.8632 {\scriptsize[-4.8832, -4.8409]} & -4.5367 {\scriptsize[-4.5587, -4.5128]} & -4.2155 {\scriptsize[-4.2404, -4.1866]} \\ | |
| 14 | +Elastic net & -5.3261 {\scriptsize[-5.3486, -5.3037]} & -4.8631 {\scriptsize[-4.8831, -4.8407]} & -4.5368 {\scriptsize[-4.5588, -4.5128]} & -4.2156 {\scriptsize[-4.2404, -4.1867]} \\ | |
| 15 | +LightGBM & -5.3289 {\scriptsize[-5.3506, -5.3063]} & -4.8551 {\scriptsize[-4.8753, -4.8326]} & -4.5411 {\scriptsize[-4.5633, -4.5180]} & -4.2191 {\scriptsize[-4.2434, -4.1914]} \\ | |
| 16 | +MLP (1m) & nan & nan & nan & nan \\ | |
| 17 | +TCN (1m) & nan & nan & nan & nan \\ | |
| 18 | +MRPT-S (1m+5m+30m) & nan & nan & nan & nan \\ | |
| 19 | +MRPT-S (1m only) & nan & nan & nan & nan \\ | |
| 20 | +MRPT-B (1m+5m+30m) & nan & nan & nan & nan \\ | |
| 21 | +\bottomrule | |
| 22 | +\end{tabular} | |
| 23 | +\begin{minipage}{0.95\textwidth}\scriptsize Cluster-bootstrap (trading-day) 95\% intervals in brackets.\end{minipage} | |
| 24 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/main_qlike.tex
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| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Main: mean QLIKE of the cumulative-return forecast by horizon (minutes)} | |
| 3 | +\label{tab:main_qlike} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Random walk (trailing RMS) & -12.3011 {\scriptsize[-12.3357, -12.2647]} & -11.2438 {\scriptsize[-11.2774, -11.2053]} & -10.5819 {\scriptsize[-10.6160, -10.5427]} & -9.9314 {\scriptsize[-9.9665, -9.8897]} \\ | |
| 9 | +Seasonal volatility & -12.3858 {\scriptsize[-12.4188, -12.3489]} & -11.3268 {\scriptsize[-11.3639, -11.2834]} & -10.6551 {\scriptsize[-10.6952, -10.6061]} & -9.9916 {\scriptsize[-10.0361, -9.9323]} \\ | |
| 10 | +EWMA-$t$ & -12.4291 {\scriptsize[-12.4603, -12.3927]} & -11.3537 {\scriptsize[-11.3907, -11.3114]} & -10.6715 {\scriptsize[-10.7094, -10.6265]} & -9.9930 {\scriptsize[-10.0339, -9.9413]} \\ | |
| 11 | +HAR-RV & -12.2819 {\scriptsize[-12.3137, -12.2475]} & -11.3605 {\scriptsize[-11.4055, -11.3071]} & -10.6947 {\scriptsize[-10.7386, -10.6459]} & -10.0465 {\scriptsize[-10.0884, -9.9945]} \\ | |
| 12 | +GARCH(1,1)-$t$ & -12.3390 {\scriptsize[-12.3766, -12.2971]} & -11.2731 {\scriptsize[-11.3120, -11.2289]} & -10.5920 {\scriptsize[-10.6309, -10.5470]} & -9.9059 {\scriptsize[-9.9462, -9.8580]} \\ | |
| 13 | +Ridge & -12.2468 {\scriptsize[-12.2897, -12.2033]} & -11.3655 {\scriptsize[-11.4057, -11.3170]} & -10.7071 {\scriptsize[-10.7479, -10.6570]} & -10.0542 {\scriptsize[-10.0979, -9.9984]} \\ | |
| 14 | +Elastic net & -12.2460 {\scriptsize[-12.2890, -12.2026]} & -11.3651 {\scriptsize[-11.4051, -11.3165]} & -10.7066 {\scriptsize[-10.7475, -10.6563]} & -10.0537 {\scriptsize[-10.0974, -9.9978]} \\ | |
| 15 | +LightGBM & 5.8416 {\scriptsize[-1.1419, 14.3811]} & -11.1290 {\scriptsize[-11.3556, -10.8016]} & -10.7147 {\scriptsize[-10.7553, -10.6689]} & -10.0661 {\scriptsize[-10.1063, -10.0165]} \\ | |
| 16 | +MLP (1m) & -12.4593 {\scriptsize[-12.4939, -12.4208]} & -11.3889 {\scriptsize[-11.4249, -11.3434]} & -10.7168 {\scriptsize[-10.7542, -10.6698]} & -10.0558 {\scriptsize[-10.0975, -10.0073]} \\ | |
| 17 | +TCN (1m) & -12.4704 {\scriptsize[-12.5018, -12.4332]} & -11.3940 {\scriptsize[-11.4310, -11.3510]} & -10.7198 {\scriptsize[-10.7598, -10.6741]} & -10.0619 {\scriptsize[-10.1020, -10.0151]} \\ | |
| 18 | +MRPT-S (1m+5m+30m) & -12.4763 {\scriptsize[-12.5080, -12.4395]} & -11.4077 {\scriptsize[-11.4437, -11.3669]} & -10.7366 {\scriptsize[-10.7742, -10.6941]} & -10.0795 {\scriptsize[-10.1178, -10.0350]} \\ | |
| 19 | +MRPT-S (1m only) & -12.4730 {\scriptsize[-12.5048, -12.4358]} & -11.4028 {\scriptsize[-11.4405, -11.3594]} & -10.7305 {\scriptsize[-10.7695, -10.6850]} & -10.0715 {\scriptsize[-10.1112, -10.0212]} \\ | |
| 20 | +MRPT-B (1m+5m+30m) & -12.4727 {\scriptsize[-12.5044, -12.4354]} & -11.4041 {\scriptsize[-11.4413, -11.3610]} & -10.7327 {\scriptsize[-10.7716, -10.6880]} & -10.0748 {\scriptsize[-10.1147, -10.0255]} \\ | |
| 21 | +\bottomrule | |
| 22 | +\end{tabular} | |
| 23 | +\begin{minipage}{0.95\textwidth}\scriptsize Cluster-bootstrap (trading-day) 95\% intervals in brackets.\end{minipage} | |
| 24 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/main_wis.tex
+24 −0
@@ -0,0 +1,24 @@ | ||
| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Main: mean WIS of the cumulative-return forecast by horizon (minutes)} | |
| 3 | +\label{tab:main_wis} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Random walk (trailing RMS) & 0.0007 {\scriptsize[0.0007, 0.0008]} & 0.0013 {\scriptsize[0.0012, 0.0013]} & 0.0017 {\scriptsize[0.0017, 0.0018]} & 0.0024 {\scriptsize[0.0023, 0.0024]} \\ | |
| 9 | +Seasonal volatility & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0024]} \\ | |
| 10 | +EWMA-$t$ & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0024]} \\ | |
| 11 | +HAR-RV & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0023]} \\ | |
| 12 | +GARCH(1,1)-$t$ & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0024]} \\ | |
| 13 | +Ridge & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0023]} \\ | |
| 14 | +Elastic net & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0023]} \\ | |
| 15 | +LightGBM & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0023]} \\ | |
| 16 | +MLP (1m) & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0023]} \\ | |
| 17 | +TCN (1m) & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0023]} \\ | |
| 18 | +MRPT-S (1m+5m+30m) & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0023]} \\ | |
| 19 | +MRPT-S (1m only) & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0023]} \\ | |
| 20 | +MRPT-B (1m+5m+30m) & 0.0007 {\scriptsize[0.0007, 0.0007]} & 0.0012 {\scriptsize[0.0012, 0.0012]} & 0.0017 {\scriptsize[0.0016, 0.0017]} & 0.0023 {\scriptsize[0.0022, 0.0023]} \\ | |
| 21 | +\bottomrule | |
| 22 | +\end{tabular} | |
| 23 | +\begin{minipage}{0.95\textwidth}\scriptsize Cluster-bootstrap (trading-day) 95\% intervals in brackets.\end{minipage} | |
| 24 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/pilot_calibration.tex
+23 −0
@@ -0,0 +1,23 @@ | ||
| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Pilot: empirical 50/80/95\% coverage and PIT KS statistic} | |
| 3 | +\label{tab:pilot_calib} | |
| 4 | +\begin{tabular}{lcccccccccccccccc} | |
| 5 | +\toprule | |
| 6 | +Model & \multicolumn{4}{c}{$H=5$} & \multicolumn{4}{c}{$H=15$} & \multicolumn{4}{c}{$H=30$} & \multicolumn{4}{c}{$H=60$} \\ | |
| 7 | + & 50 & 80 & 95 & KS & 50 & 80 & 95 & KS & 50 & 80 & 95 & KS & 50 & 80 & 95 & KS \\ | |
| 8 | +\midrule | |
| 9 | +Random walk (trailing RMS) & 0.62 & 0.87 & 0.96 & 0.070 & 0.61 & 0.87 & 0.96 & 0.063 & 0.60 & 0.86 & 0.96 & 0.068 & 0.61 & 0.87 & 0.97 & 0.075 \\ | |
| 10 | +Seasonal volatility & 0.53 & 0.80 & 0.94 & 0.029 & 0.53 & 0.80 & 0.94 & 0.025 & 0.52 & 0.79 & 0.93 & 0.026 & 0.52 & 0.79 & 0.93 & 0.039 \\ | |
| 11 | +EWMA-$t$ & 0.51 & 0.81 & 0.97 & 0.017 & 0.50 & 0.80 & 0.96 & 0.012 & 0.49 & 0.80 & 0.96 & 0.027 & 0.51 & 0.80 & 0.96 & 0.034 \\ | |
| 12 | +HAR-RV & 0.63 & 0.92 & 0.99 & 0.082 & 0.48 & 0.78 & 0.96 & 0.021 & 0.46 & 0.77 & 0.95 & 0.039 & 0.48 & 0.77 & 0.95 & 0.033 \\ | |
| 13 | +GARCH(1,1)-$t$ & 0.54 & 0.85 & 0.97 & 0.035 & 0.56 & 0.85 & 0.98 & 0.037 & 0.56 & 0.85 & 0.98 & 0.043 & 0.59 & 0.87 & 0.98 & 0.065 \\ | |
| 14 | +Ridge & 0.41 & 0.70 & 0.91 & 0.074 & 0.44 & 0.74 & 0.94 & 0.042 & 0.44 & 0.75 & 0.94 & 0.052 & 0.46 & 0.75 & 0.94 & 0.040 \\ | |
| 15 | +Elastic net & 0.41 & 0.71 & 0.91 & 0.075 & 0.44 & 0.74 & 0.94 & 0.041 & 0.44 & 0.74 & 0.94 & 0.053 & 0.46 & 0.75 & 0.94 & 0.038 \\ | |
| 16 | +LightGBM & 0.35 & 0.64 & 0.89 & 0.110 & 0.41 & 0.71 & 0.92 & 0.063 & 0.46 & 0.74 & 0.92 & 0.044 & 0.45 & 0.75 & 0.92 & 0.042 \\ | |
| 17 | +MLP (1m) & 0.51 & 0.80 & 0.95 & 0.021 & 0.53 & 0.81 & 0.95 & 0.024 & 0.51 & 0.80 & 0.94 & 0.030 & 0.53 & 0.80 & 0.94 & 0.043 \\ | |
| 18 | +TCN (1m) & 0.54 & 0.82 & 0.96 & 0.027 & 0.55 & 0.82 & 0.96 & 0.034 & 0.52 & 0.81 & 0.95 & 0.032 & 0.54 & 0.81 & 0.95 & 0.050 \\ | |
| 19 | +MRPT-S (1m+5m+30m) & 0.54 & 0.83 & 0.96 & 0.035 & 0.55 & 0.83 & 0.96 & 0.034 & 0.53 & 0.82 & 0.95 & 0.037 & 0.54 & 0.81 & 0.95 & 0.053 \\ | |
| 20 | +MRPT-S (1m only) & 0.55 & 0.83 & 0.96 & 0.039 & 0.56 & 0.83 & 0.96 & 0.038 & 0.53 & 0.82 & 0.95 & 0.040 & 0.54 & 0.81 & 0.95 & 0.053 \\ | |
| 21 | +\bottomrule | |
| 22 | +\end{tabular} | |
| 23 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/pilot_compare_crps.tex
+22 −0
@@ -0,0 +1,22 @@ | ||
| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Pilot: CRPS relative to Random walk (trailing RMS)} | |
| 3 | +\label{tab:pilot_cmp_crps} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Seasonal volatility & -1.98\% (-5.7) & -2.51\% (-6.6) & -2.69\% (-5.8) & -2.12\% (-3.4) \\ | |
| 9 | +EWMA-$t$ & -2.83\% (-8.1) & -2.79\% (-6.7) & -2.62\% (-5.2) & -1.77\% (-2.3) \\ | |
| 10 | +HAR-RV & -0.24\% (-0.7) & -3.20\% (-8.1) & -3.25\% (-7.0) & -3.04\% (-4.6) \\ | |
| 11 | +GARCH(1,1)-$t$ & -2.58\% (-8.9) & -2.63\% (-8.0) & -2.45\% (-7.2) & -1.60\% (-3.7) \\ | |
| 12 | +Ridge & -2.06\% (-3.7) & -3.07\% (-5.7) & -3.29\% (-5.5) & -2.96\% (-4.1) \\ | |
| 13 | +Elastic net & -2.14\% (-3.8) & -3.10\% (-5.8) & -3.31\% (-5.6) & -2.91\% (-3.9) \\ | |
| 14 | +LightGBM & +3.20\% (3.7) & +1.62\% (2.0) & +1.59\% (1.5) & +2.49\% (1.8) \\ | |
| 15 | +MLP (1m) & -3.08\% (-9.1) & -2.96\% (-8.3) & -3.01\% (-7.2) & -2.47\% (-4.2) \\ | |
| 16 | +TCN (1m) & -3.11\% (-9.8) & -2.94\% (-7.8) & -3.16\% (-7.3) & -2.50\% (-4.0) \\ | |
| 17 | +MRPT-S (1m+5m+30m) & -2.96\% (-8.8) & -3.07\% (-7.9) & -3.36\% (-7.2) & -2.62\% (-4.2) \\ | |
| 18 | +MRPT-S (1m only) & -3.00\% (-8.9) & -2.99\% (-7.8) & -3.16\% (-6.8) & -2.42\% (-3.9) \\ | |
| 19 | +\bottomrule | |
| 20 | +\end{tabular} | |
| 21 | +\begin{minipage}{0.95\textwidth}\scriptsize Relative change in mean CRPS versus the reference (negative = better); Diebold--Mariano $t$-statistic with HAC variance in parentheses.\end{minipage} | |
| 22 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/pilot_compare_qlike.tex
+22 −0
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| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Pilot: QLIKE relative to Random walk (trailing RMS)} | |
| 3 | +\label{tab:pilot_cmp_qlike} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Seasonal volatility & -6631047621301.96\% (-3.7) & -9798545943930.17\% (-6.7) & -8922777889662.27\% (-5.8) & -8074565519238.53\% (-4.6) \\ | |
| 9 | +EWMA-$t$ & -12554922968119.03\% (-8.8) & -11610326741044.22\% (-8.6) & -9962403507408.67\% (-6.7) & -7537309379639.13\% (-3.7) \\ | |
| 10 | +HAR-RV & +7877866372961.78\% (4.6) & -14099293226631.73\% (-13.0) & -13394448504861.81\% (-10.4) & -12560029461854.98\% (-8.0) \\ | |
| 11 | +GARCH(1,1)-$t$ & -6845837520747.71\% (-5.6) & -4710411807615.16\% (-4.2) & -1671497472176.46\% (-1.3) & +4026232839171.85\% (2.9) \\ | |
| 12 | +Ridge & -2945713870141.00\% (-1.4) & -14078646030114.02\% (-11.7) & -13850072137900.00\% (-9.9) & -13521968596908.26\% (-8.3) \\ | |
| 13 | +Elastic net & -2906922453727.77\% (-1.4) & -14052357953211.58\% (-11.7) & -13800380130330.72\% (-9.9) & -13480669954535.19\% (-8.2) \\ | |
| 14 | +LightGBM & +80780260086423.78\% (1.4) & -12012831272926.51\% (-7.3) & -12181626304741.97\% (-7.1) & -11572312577415.51\% (-6.0) \\ | |
| 15 | +MLP (1m) & -13608727182964.57\% (-13.2) & -13379373428123.78\% (-13.6) & -13042336995340.29\% (-11.2) & -12126414938724.40\% (-8.1) \\ | |
| 16 | +TCN (1m) & -13969630443261.25\% (-13.3) & -13939960177831.86\% (-13.9) & -13400649669390.51\% (-12.0) & -12492078176605.08\% (-8.7) \\ | |
| 17 | +MRPT-S (1m+5m+30m) & -14426818050181.94\% (-11.8) & -14161537101518.33\% (-13.4) & -13449231005232.20\% (-12.1) & -12662443344111.06\% (-9.2) \\ | |
| 18 | +MRPT-S (1m only) & -13769052086011.91\% (-11.5) & -13594106578801.23\% (-13.2) & -12903146151897.46\% (-11.4) & -12091461273483.05\% (-8.3) \\ | |
| 19 | +\bottomrule | |
| 20 | +\end{tabular} | |
| 21 | +\begin{minipage}{0.95\textwidth}\scriptsize Relative change in mean QLIKE versus the reference (negative = better); Diebold--Mariano $t$-statistic with HAC variance in parentheses.\end{minipage} | |
| 22 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/pilot_compare_wis.tex
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| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Pilot: WIS relative to Random walk (trailing RMS)} | |
| 3 | +\label{tab:pilot_cmp_wis} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Seasonal volatility & -1.98\% (-5.1) & -2.60\% (-6.2) & -2.77\% (-5.3) & -2.12\% (-3.1) \\ | |
| 9 | +EWMA-$t$ & -2.82\% (-7.5) & -2.86\% (-6.4) & -2.69\% (-5.1) & -1.70\% (-2.1) \\ | |
| 10 | +HAR-RV & +0.12\% (0.3) & -3.34\% (-8.1) & -3.44\% (-7.1) & -3.16\% (-4.5) \\ | |
| 11 | +GARCH(1,1)-$t$ & -2.56\% (-8.4) & -2.59\% (-7.4) & -2.45\% (-6.7) & -1.43\% (-3.1) \\ | |
| 12 | +Ridge & -2.06\% (-3.4) & -3.26\% (-5.8) & -3.55\% (-5.7) & -3.14\% (-4.2) \\ | |
| 13 | +Elastic net & -2.12\% (-3.5) & -3.30\% (-6.0) & -3.55\% (-5.7) & -3.07\% (-4.0) \\ | |
| 14 | +LightGBM & +3.37\% (3.7) & +1.49\% (1.8) & +1.39\% (1.3) & +2.43\% (1.7) \\ | |
| 15 | +MLP (1m) & -3.24\% (-9.0) & -3.15\% (-8.3) & -3.23\% (-7.3) & -2.59\% (-4.1) \\ | |
| 16 | +TCN (1m) & -3.25\% (-9.7) & -3.15\% (-7.9) & -3.41\% (-7.4) & -2.64\% (-3.9) \\ | |
| 17 | +MRPT-S (1m+5m+30m) & -3.13\% (-8.7) & -3.29\% (-8.1) & -3.57\% (-7.3) & -2.78\% (-4.2) \\ | |
| 18 | +MRPT-S (1m only) & -3.13\% (-8.7) & -3.20\% (-7.9) & -3.39\% (-6.9) & -2.53\% (-3.8) \\ | |
| 19 | +\bottomrule | |
| 20 | +\end{tabular} | |
| 21 | +\begin{minipage}{0.95\textwidth}\scriptsize Relative change in mean WIS versus the reference (negative = better); Diebold--Mariano $t$-statistic with HAC variance in parentheses.\end{minipage} | |
| 22 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/pilot_crps_scaled.tex
+23 −0
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| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Pilot: mean scaled CRPS of the cumulative-return forecast by horizon (minutes)} | |
| 3 | +\label{tab:pilot_crps_scaled} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Random walk (trailing RMS) & 0.4803 {\scriptsize[0.4618, 0.5012]} & 0.4874 {\scriptsize[0.4641, 0.5093]} & 0.4952 {\scriptsize[0.4688, 0.5225]} & 0.4819 {\scriptsize[0.4381, 0.5395]} \\ | |
| 9 | +Seasonal volatility & 0.4746 {\scriptsize[0.4545, 0.4957]} & 0.4793 {\scriptsize[0.4526, 0.5047]} & 0.4870 {\scriptsize[0.4569, 0.5190]} & 0.4767 {\scriptsize[0.4268, 0.5419]} \\ | |
| 10 | +EWMA-$t$ & 0.4699 {\scriptsize[0.4502, 0.4912]} & 0.4775 {\scriptsize[0.4517, 0.5023]} & 0.4868 {\scriptsize[0.4561, 0.5196]} & 0.4773 {\scriptsize[0.4276, 0.5428]} \\ | |
| 11 | +HAR-RV & 0.4833 {\scriptsize[0.4648, 0.5032]} & 0.4761 {\scriptsize[0.4492, 0.5019]} & 0.4845 {\scriptsize[0.4540, 0.5168]} & 0.4728 {\scriptsize[0.4223, 0.5391]} \\ | |
| 12 | +GARCH(1,1)-$t$ & 0.4714 {\scriptsize[0.4522, 0.4932]} & 0.4783 {\scriptsize[0.4545, 0.5018]} & 0.4876 {\scriptsize[0.4602, 0.5167]} & 0.4789 {\scriptsize[0.4331, 0.5388]} \\ | |
| 13 | +Ridge & 0.4734 {\scriptsize[0.4518, 0.4968]} & 0.4765 {\scriptsize[0.4494, 0.5028]} & 0.4842 {\scriptsize[0.4533, 0.5170]} & 0.4723 {\scriptsize[0.4216, 0.5368]} \\ | |
| 14 | +Elastic net & 0.4732 {\scriptsize[0.4516, 0.4967]} & 0.4764 {\scriptsize[0.4494, 0.5026]} & 0.4841 {\scriptsize[0.4532, 0.5169]} & 0.4725 {\scriptsize[0.4217, 0.5371]} \\ | |
| 15 | +LightGBM & 0.5090 {\scriptsize[0.4871, 0.5325]} & 0.5034 {\scriptsize[0.4756, 0.5308]} & 0.5116 {\scriptsize[0.4812, 0.5471]} & 0.5019 {\scriptsize[0.4484, 0.5765]} \\ | |
| 16 | +MLP (1m) & 0.4689 {\scriptsize[0.4497, 0.4908]} & 0.4769 {\scriptsize[0.4522, 0.5015]} & 0.4847 {\scriptsize[0.4559, 0.5157]} & 0.4743 {\scriptsize[0.4250, 0.5390]} \\ | |
| 17 | +TCN (1m) & 0.4687 {\scriptsize[0.4497, 0.4896]} & 0.4767 {\scriptsize[0.4526, 0.5008]} & 0.4838 {\scriptsize[0.4552, 0.5144]} & 0.4743 {\scriptsize[0.4252, 0.5388]} \\ | |
| 18 | +MRPT-S (1m+5m+30m) & 0.4697 {\scriptsize[0.4509, 0.4903]} & 0.4763 {\scriptsize[0.4526, 0.5001]} & 0.4831 {\scriptsize[0.4553, 0.5135]} & 0.4736 {\scriptsize[0.4238, 0.5381]} \\ | |
| 19 | +MRPT-S (1m only) & 0.4693 {\scriptsize[0.4506, 0.4899]} & 0.4765 {\scriptsize[0.4527, 0.5006]} & 0.4842 {\scriptsize[0.4558, 0.5148]} & 0.4745 {\scriptsize[0.4245, 0.5395]} \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| 22 | +\begin{minipage}{0.95\textwidth}\scriptsize Cluster-bootstrap (trading-day) 95\% intervals in brackets.\end{minipage} | |
| 23 | +\end{table} | |
| \ No newline at end of file | ||
added
paper/tables/pilot_logscore.tex
+23 −0
@@ -0,0 +1,23 @@ | ||
| 1 | +\begin{table}[htbp]\centering\small | |
| 2 | +\caption{Pilot: mean log score of the cumulative-return forecast by horizon (minutes)} | |
| 3 | +\label{tab:pilot_logscore} | |
| 4 | +\begin{tabular}{lcccc} | |
| 5 | +\toprule | |
| 6 | +Model & $H=5$ & $H=15$ & $H=30$ & $H=60$ \\ | |
| 7 | +\midrule | |
| 8 | +Random walk (trailing RMS) & nan & nan & nan & nan \\ | |
| 9 | +Seasonal volatility & nan & nan & nan & nan \\ | |
| 10 | +EWMA-$t$ & -5.2979 {\scriptsize[-5.3501, -5.2489]} & -4.7338 {\scriptsize[-4.7970, -4.6663]} & -4.3653 {\scriptsize[-4.4434, -4.2821]} & -4.0215 {\scriptsize[-4.1344, -3.8696]} \\ | |
| 11 | +HAR-RV & -5.2318 {\scriptsize[-5.2750, -5.1939]} & -4.7437 {\scriptsize[-4.8070, -4.6722]} & -4.3804 {\scriptsize[-4.4598, -4.2939]} & -4.0439 {\scriptsize[-4.1592, -3.8939]} \\ | |
| 12 | +GARCH(1,1)-$t$ & -5.2893 {\scriptsize[-5.3330, -5.2481]} & -4.7274 {\scriptsize[-4.7788, -4.6722]} & -4.3585 {\scriptsize[-4.4205, -4.2937]} & -4.0114 {\scriptsize[-4.0946, -3.8983]} \\ | |
| 13 | +Ridge & -5.2731 {\scriptsize[-5.3350, -5.2135]} & -4.7400 {\scriptsize[-4.8076, -4.6674]} & -4.3819 {\scriptsize[-4.4641, -4.2950]} & -4.0459 {\scriptsize[-4.1620, -3.8925]} \\ | |
| 14 | +Elastic net & -5.2733 {\scriptsize[-5.3355, -5.2137]} & -4.7402 {\scriptsize[-4.8078, -4.6676]} & -4.3817 {\scriptsize[-4.4639, -4.2949]} & -4.0457 {\scriptsize[-4.1620, -3.8920]} \\ | |
| 15 | +LightGBM & -5.1540 {\scriptsize[-5.2276, -5.0829]} & -4.6712 {\scriptsize[-4.7450, -4.5915]} & -4.3235 {\scriptsize[-4.4092, -4.2250]} & -3.9773 {\scriptsize[-4.1001, -3.8019]} \\ | |
| 16 | +MLP (1m) & nan & nan & nan & nan \\ | |
| 17 | +TCN (1m) & nan & nan & nan & nan \\ | |
| 18 | +MRPT-S (1m+5m+30m) & nan & nan & nan & nan \\ | |
| 19 | +MRPT-S (1m only) & nan & nan & nan & nan \\ | |
| 20 | +\bottomrule | |
| 21 | +\end{tabular} | |
| 22 | +\begin{minipage}{0.95\textwidth}\scriptsize Cluster-bootstrap (trading-day) 95\% intervals in brackets.\end{minipage} | |
| 23 | +\end{table} | |
| \ No newline at end of file | ||
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