UQO Working Paper No. 12· v0.3· November 2026· 83 pages

Forecasting Realized Volatility Across Asset Classes

HAR, GARCH, and Machine Learning in a Unified Multi-Asset Horse Race, 2013–2026

Finance & Economics

The benchmark matters more than the learner: log-HAR lowers HAR's one-day QLIKE by 25 percent (10 percent at the median), and against it the machine-learning gain is a one-day gain, significant on 64 percent of instruments and a tie at one month.

33 forecasts, from HAR and GARCH to penalized regressions, tree ensembles, deep learners and combinations, are raced under one protocol on 25 equities and ETFs, currency pairs, cryptocurrencies and futures. A pooled model transfers to instruments it has never seen at one day. Statistical accuracy does not translate into a measurable economic advantage in volatility timing net of costs, and the deep-learning verdict is conditional on single-asset training.

Simon-Pierre Boucher — contact@spboucher.ai

Paper PDF (revised)Read online Code & data repository

−25% (−10% median)

One-day mean QLIKE of log-HAR relative to HAR in levels, lower on all 25 instruments; the mean is dominated by a few instruments on which HAR in levels collapses (ratios of 0.34 for IWM and 0.30 for BTC), and the gain shrinks as the estimation window lengthens.

64% / 12% / 4%

Share of instruments on which ridge on the extended predictor set is significantly better than log-HAR at one day, one week and one month (panel t = −4.88, −2.29, −0.09): a one-day gain and a tie at the monthly horizon. The gain comes from the predictors, not the estimator.

64% and 92%

Share of instruments on which LightGBM on the extended set and the single-asset LSTM are significantly worse than log-HAR at one day; pooling the trees across instruments brings them to the level of log-HAR at one day and no further.

0.937, 19 of 25

Median one-day QLIKE ratio to HAR of a pooled LightGBM re-estimated without the target instrument and without its identifier, and the number of instruments on which it beats HAR; identity is worth about 4 percent of QLIKE at one day and nothing at one month.

p = 0.23

Smallest p-value for any forecaster against a turnover-free trailing-variance rule in volatility timing net of costs, under the panel statistic that accounts for common dates; cross-instrument intervals, which treat instruments as independent, exclude zero for 28 of 72 model–band pairs.

0.028 (s.e. 0.015)

Paired net Sharpe difference of the LSTM, the highest-ranked forecaster in volatility timing net of 5 basis points, against HAR; it shrinks to 0.002 with a 20 percent no-trade band.

23% → 63% / 60%

Share of instrument–model pairs passing the 1 percent VaR unconditional-coverage test with a Gaussian quantile versus a Student-t or filtered-historical-simulation quantile; no model passes on 80 percent or more of the instruments under any tail.

Abstract

Which volatility forecaster should a multi-asset investor use, against which benchmark? One out-of-sample race of 33 forecasts—from HAR and GARCH to penalized regressions, tree ensembles, deep learners and combinations—is run under one protocol on 25 instruments from four asset classes, 2013–2026. Log-HAR is the relevant benchmark, lowering HAR's QLIKE by 25 percent (10 percent at the median). Ridge regression on extended predictors beats log-HAR significantly on 64 percent of instruments at one day but ties it at one month; LightGBM and single-asset deep learners are significantly worse on most instruments. A pooled model transfers to unseen instruments at one day. Net of costs, no forecaster beats a turnover-free trailing-variance rule under a panel statistic robust to common dates (smallest p = 0.23), although cross-instrument intervals exclude zero for 28 of 72 model–band pairs; a fat-tailed quantile restores one-percent VaR coverage for 60–63 percent of instrument–model pairs.

JEL: C22, C45, C53, G17

Key Results

One protocol across four asset classes

The target, rolling scheme, losses and inference are held fixed across equities and ETFs, FX, cryptocurrencies and futures, extending single-market races; the ranking those races disagree about is stable across classes while the size of the gain is not.

Log-HAR as the benchmark

Forecasting log realized variance with a retransformation accounts for most of the machine-learning gain in every class; penalized linear learners on an extended information set add about 5 QLIKE points at one day only. The paper presents this as a cross-class replication of known remedies, not a discovery.

A cross-class leave-one-out transfer test

A pooled tree learner is re-estimated with each instrument excluded and its ticker identifier dropped, extending universal-model results beyond equities; volatility dynamics transfer at one day.

Economic value with paired inference

Every forecaster is carried through to volatility timing with transaction costs, no-trade bands, a turnover-free benchmark and paired inference, and to Value-at-Risk under Gaussian, Student-t and filtered-historical-simulation quantiles.

Quality control

This paper went through a multi-stage quality control: 6 quality-control reports and 85 points checked. The version presented on this page is the revised manuscript. Scores are on a 0–100 scale and are a diagnostic of the manuscript, not an acceptance probability.

Score after revision

67.1/100

56.0 before quality control · +11.1

Quality control dated November 4, 2026

Quality-control decision: major revision
Scientific integrity: PASS
Reproducibility: R1reproduced from documented analysis data
Maturity: Bone revision cycle from submission
Quality-control reports: 6
Points checked: 85

Scores by dimension

Before quality controlAfter revision

Originality & contribution57.0 → 58.0
Scientific rigor56.2 → 68.0
Identification & methodology52.2 → 68.0
Data & reproducibility52.5 → 70.0
Robustness & validation56.0 → 70.0
Writing67.5 → 72.0
Figures & tables62.2 → 69.0
Literature positioning59.2 → 75.0

Revised manuscript83 pages12 figures26 tables26 equations91 references35,227 words

What quality control changed

Quality control moved the benchmark from HAR in levels to log-HAR, against which the machine-learning gain is confined to the one-day horizon. Three earlier claims were withdrawn after errors were found: the one-month lead of a forecast combination, the failure of cross-asset transfer, and the conclusion that smooth forecasters beat accurate ones in volatility timing. A time-stamp error in the cryptocurrency data was also corrected and the affected forecasts re-run.

Benchmark: ridge on extended predictors beats HAR on 24 of 25 instruments → against log-HAR it is significantly better on 64 percent of instruments at one day, 12 percent at one week and 4 percent at one month.
Forecast combination: the inverse-MSE combination led at one month → withdrawn; its weights used targets not yet realized at the forecast origin.
Transfer to unseen assets: fails outside a homogeneous class → a pooled model without the target's identity has a median one-day QLIKE ratio to HAR of 0.937 and beats HAR on 19 of 25 instruments; the earlier collapse was an encoding artefact.
Volatility timing: smooth forecasters earn more than accurate ones net of costs → no forecaster beats a turnover-free trailing-variance rule under the panel statistic (smallest p = 0.23).
Value-at-Risk at 1 percent: no forecaster is calibrated → the Gaussian quantile passes on 23 percent of instrument–model pairs, a Student-t or filtered-historical-simulation quantile on 63 and 60 percent.
Cryptocurrency time stamps: treated as Eastern → established as UTC; same-day FX and futures predictors of crypto targets are now lagged one day, and no conclusion changed.

Limitations stated in the paper

The cryptocurrency bars are not tick-cleaned; a bar-level filter would reduce the crypto gains further rather than enlarge them.
The deep learners are trained instrument by instrument, with one seed on 21 of the 25 instruments, and no pooled network was trained, so the deep-learning rows are a lower bound on what sequence models can do.
Window-length sensitivity was run at one re-estimation frequency, and jump statistics are biased upward for instruments with frequent zero 5-minute returns.
The raw data source has been retired and cannot be redistributed; the inputs are documented by checksums and archived, and the derived daily panel awaits a licence decision before deposit.

Read online (interactive reader)Revised PDF Revised branch on spbgit

Data

1-minute bars for 25 instruments, January 2013 – July 2026

Five ETFs and five large-capitalization stocks, five major currency pairs, five cryptocurrencies (BTC, ETH, SOL, ADA, XRP) and five continuous front-month futures (ES, NQ, CL, GC, ZN), plus the VIX as a predictor, downloaded on 10 August 2026 from the HF Market Data API. The pipeline processes 84.2 million 1-minute bars and produces a panel of 84,898 asset-days of realized measures.

Sessions and time stamps

Equities and ETFs use regular trading hours; FX and futures use the Eastern calendar day; cryptocurrency bars are stamped in UTC and use the UTC day, as established by an audit against public exchange candles. Days with too few valid bars are discarded and no further bar cleaning is applied.

Common evaluation sample

59,798 asset-days at one day (59,606 at five days, 58,776 at 22 days) on which all 33 forecasts exist, starting in November 2016 for the series that begin in 2013 and later for the altcoins. Mean losses are computed per instrument and then averaged across the 25 instruments.

Methodology

Target and rolling protocol

Average subsampled 5-minute realized variance over the next 1, 5 and 22 trading days; 1,000-day rolling estimation window, re-estimation every 22 days, daily forecasts, with estimation samples restricted to fully realized targets.

Thirty-three forecasts

Eleven HAR specifications (including HARQ, the semivariance HAR, a weighted-least-squares HAR and log-HAR), GARCH, GJR, EGARCH and Realized GARCH, thirteen penalized regressions and tree ensembles on the HAR set and on eighteen extended predictors, an LSTM and a Transformer encoder, a LightGBM pooled across instruments, and two combinations.

Forecast evaluation

QLIKE and MSE losses; Diebold–Mariano tests against three benchmarks (HAR in levels, log-HAR, ridge on the HAR set) with HAC variances, multiplicity adjustments across instruments and a panel statistic; model confidence sets; calibration, encompassing and fluctuation tests.

Robustness

Sub-periods, estimation-window length, alternative realized measures, implausible cryptocurrency days, leave-one-instrument-out transfer and random seeds.

Economic value

Volatility timing with transaction costs, no-trade bands and a turnover-free trailing-variance benchmark, utility gains, and 1 and 5 percent Value-at-Risk backtests under three tail assumptions.

Reproducibility

The replication package runs from one entry point with per-step logs under a pinned Python environment: it verifies the data manifest, builds the realized measures, produces the forecasts, runs the evaluation, robustness and economic-value blocks and generates every figure and table.

Numbers quoted in the text are macros written from the same outputs; thirty-nine unit and regression tests cover the chronology of every information set and the reproduction of the evaluation layer.

The data service was retired on 2 October 2026 and its terms do not permit redistribution of the raw bars; the package documents the inputs with a manifest of checksums, sizes, row counts and timestamps, and an archived copy of the cache is available to replicators on request.

An appendix corrigendum records the values that changed when the cross-asset predictors of the cryptocurrency targets were lagged by one day.

Realized GARCH and multi-step EGARCH forecasts differ at the fourth significant digit across processor architectures, and LSTM training on the GPU is not bitwise deterministic.

Cite this paper

Boucher, S.-P. (2026). Forecasting Realized Volatility Across Asset Classes. UQO Working Paper No. 12, Université du Québec en Outaouais.

@techreport{boucher2026wp12,
  author      = {Simon-Pierre Boucher},
  title       = {Forecasting Realized Volatility Across Asset Classes},
  institution = {Université du Québec en Outaouais, Département des sciences administratives},
  number      = {12},
  type        = {UQO Working Paper},
  year        = {2026},
  month       = {nov},
  url         = {https://www.spboucher.ai/research/wp12},
}