UQO Working Papers · WP12 · v0.2
Forecasting Realized Volatility Across Asset Classes: HAR, GARCH, and Machine Learning in a Unified Multi-Asset Horse Race, 2013–2026
- Year
- 2026
- First release
- October 2026
- Latest revision
- October 2026
- Publication status
- Working paper
Most of the machine-learning gain over HAR is just taking logs
On a common sample of 59,323 asset-days, log-HAR lowers HAR's one-day QLIKE by 25% on every instrument and ridge on an extended predictor set is the best forecaster (ratio 0.70); trees and deep learners trail, and the most accurate forecasters lose money net of costs.
Abstract
The paper compares 27 forecasts of daily realized variance (six HAR specifications, GARCH, GJR, EGARCH and Realized GARCH, penalized regressions, random forests, XGBoost and LightGBM on two information sets, an LSTM, a Transformer, a LightGBM pooled across assets, and two combinations) on 25 liquid instruments from four asset classes (equities and ETFs, FX, cryptocurrencies, futures) over 2013–2026, under one protocol: the same subsampled 5-minute realized-variance target, a 1,000-day rolling window, horizons of 1, 5 and 22 days, QLIKE and MSE losses, Diebold–Mariano tests, model confidence sets, and a common evaluation sample of 59,323 asset-days.
Log-linear models dominate: log-HAR lowers the QLIKE of HAR in levels by 25% at one day on every instrument, and ridge regression on an extended predictor set is the best individual forecaster (ratio 0.70), significantly better than HAR on 24 of 25 instruments. Tree ensembles and deep learners trail the linear learners and fall behind HAR at one month; pooling across assets helps the trees but does not transfer to unseen assets outside a homogeneous class. Gains are largest for cryptocurrencies (0.62) and smallest for FX (0.85), grow with the noise of the realized measure, and shrink in the calm 2024–2026 period.
In volatility timing net of 5 basis points, smooth forecasters (LSTM, GARCH) earn higher Sharpe ratios and positive utility gains over HAR than the most accurate ones, which trade too much; at the 5% VaR level all forecasters are calibrated, at 1% none is. Version 0.2 is a complete working draft: window-length sensitivity and a tick-level cleaning of the cryptocurrency bars remain to be run.
Key findings
27
forecasting models raced under one protocol
25
instruments from four asset classes, 2013–2026
59,323
asset-days in the common evaluation sample
−25%
one-day QLIKE of log-HAR relative to HAR, all instruments
0.70
QLIKE ratio of ridge (extended set) to HAR
24 / 25
instruments where ridge beats HAR significantly
Scientific contributions
- One design across four asset classes
- The same 5-minute subsampled target, 1,000-day rolling window, three horizons, losses, inference and common sample are applied to equities and ETFs, FX, cryptocurrencies and futures, so the HAR-versus-machine-learning disagreement in the literature is tested on comparable terms.
- The log transformation explains most of the gain
- Log-HAR achieves QLIKE ratios of 0.75, 0.63 and 0.79 to HAR at 1, 5 and 22 days and lower loss on 25 of 25 instruments at one day; ridge on 18 predictors adds about five points more (0.70) and is in the 90% model confidence set for every instrument.
- Nonlinear learners do not pay
- Random forests, XGBoost and LightGBM (ratios 0.79–0.85 at one day, 0.95–1.16 at one month), the LSTM (1.33) and the Transformer (1.89) are worse than the linear learners everywhere; pooling across assets rescues the trees but transfer to an unseen asset works only within FX.
- Gains track the noise of volatility
- The ridge-to-HAR ratio is 0.62 for cryptocurrencies, 0.72 for equities, 0.78 for futures and 0.85 for FX; it rises from 0.51 before 2020 to 0.88 in 2024–2026 and from 0.43 with 1-minute RV to 0.86 with a realized kernel.
- Accuracy and economic value diverge
- Net of 5 basis points the LSTM (Sharpe 0.38) and daily GARCH (0.35) beat HAR (0.34) in volatility timing while ridge (0.30) and LightGBM (0.26) trade too much, losing 47 to 121 basis points a year relative to HAR; at 5% VaR every forecaster is calibrated, at 1% all fail.
- Code corrections that changed the GARCH results
- The revision found and fixed frozen GARCH forecasts between re-estimations, a one-day conditioning lag, a mis-studentised model confidence set, a missing insanity filter on the GARCH family and a collapsed common sample; the econometric family was re-run three times.
Methodology
Methodology (4)
Realized measures and target
Subsampled 5-minute realized variance as the common target, with realized kernel (Parzen), bipower variation, tripower and realized quarticity, BNS jump tests and semivariances computed in src/wp12/realized_vol.py.
Econometric and machine-learning forecasters
HAR, HAR-J, HAR-CJ, SHAR, HARQ and log-HAR as direct projections; GARCH, GJR and EGARCH refiltered daily with an RV-unit mapping; Realized GARCH by QML; ridge, LASSO, elastic net, random forest, XGBoost and LightGBM on the HAR set and an extended 18-predictor set with walk-forward tuning; LSTM and Transformer with quarterly refits; a pooled LightGBM with asset identifiers; mean and inverse-MSE combinations.
Rolling out-of-sample evaluation
1,000-day rolling windows refit every 22 days, horizons of 1, 5 and 22 days, QLIKE and MSE on a common sample per asset and horizon, Diebold–Mariano tests with Bartlett bandwidth, model confidence sets (T_max, stationary bootstrap, 5,000 draws), Mincer–Zarnowitz and encompassing regressions.
Robustness and economic value
Sub-periods, alternative RV measures, implausible crypto days, leave-one-asset-out transfer and Giacomini–Rossi fluctuation tests; volatility timing with a 10% target and 0–20 basis-point costs, Fleming–Kirby–Ostdiek utility gains, and 1% and 5% VaR backtests with Kupiec and Christoffersen tests.
Research data
- HF Market Data 1-minute bars, 25 instruments
- 93.8 million 1-minute bars plus daily bars for 25 assets and the VIX, 1 January 2013 to 31 July 2026, from the HF Market Data API (1.6 GB parquet cache, not committed); equities use regular trading hours, futures, FX and crypto the Eastern calendar day. The headline target is 5-minute subsampled realized variance (five offset grids); 1-minute RV, realized kernel, bipower variation, quarticities, jumps and semivariances are alternatives. Panel of 84,898 asset-days before the common-sample restriction.
Reproducibility
- Nine numbered scripts from data download to paper build (01_download_data … 09_build_paper), driven by config.yaml; 91_key_numbers.py prints every number quoted in the text
- 18 pytest tests on the realized-measure and evaluation code; 25 result CSVs, 12 generated LaTeX tables and 9 figures
- Pipeline re-executed end to end on 2026-10-17 for the econometric, pooled and evaluation stages; tabular ML and deep forecasts reused from the August 2026 run with unchanged code
- Full LaTeX source with 73 Crossref-verified references (docs/bib-verification.csv); open items for version 1.0 listed in the README and conclusion
Research artifacts
Version history
| Version | Date | Description | File |
|---|---|---|---|
| v0.2current | October 2026 | Current manuscript as published on www.spboucher.ai (revised edition after the 2026-10-17 scientific review for papers 1–17). | PDF · 50 p. |