Forecasting Realized Volatility with Time Series Foundation Models: A Comparison with Econometric Benchmarks
Author: Alessio Brini (alessio.brini@duke.edu)
Paper: arXiv:2607.05291
We evaluate nine zero-shot time series foundation models (TSFMs), spanning eight distinct architectures, against eight econometric specifications for forecasting realized volatility on 50 assets from the VOLARE dataset (equities, FX, futures) at horizons of 1, 5, and 22 days. We apply Diebold-Mariano tests, the Model Confidence Set, Mincer-Zarnowitz regressions, and Giacomini-Rossi fluctuation tests.
Key findings:
- Foundation models do not deliver a uniform gain over the econometric benchmarks. Pooled QLIKE losses appear to favor several TSFMs, but the advantage is concentrated in a few outlier assets.
- Under average per-asset QLIKE loss ratios relative to Log-HAR, which weight each asset equally, only Tiny Time Mixers (TTM), the smallest model in the study (<1M parameters), beats Log-HAR at every horizon, and by a narrow margin (roughly 1.3-1.8%). The other eight TSFMs do not improve on a well-specified Log-HAR, and the econometric benchmarks (HAR, ARFIMA, ARMA, MEM) remain competitive throughout.
- A Mincer-Zarnowitz recalibration shows that much of the short-horizon edge reflects better-scaled forecasts rather than better prediction of volatility dynamics; a genuine informational gain remains only at the monthly horizon.
- A simple equal-weight average of TTM and Log-HAR matches the best single model and enters the Model Confidence Set for 98-100% of assets, so a forecaster need not identify the best model for each asset in advance.
- Performance varies so widely across TSFM architectures that which TSFM one chooses matters more than the broader choice between foundation and econometric models.
code/
config.py # Central configuration (paths, walk-forward params, model IDs)
data_loader.py # VOLARE long-format CSV loader
features.py # HAR regressor construction
utils.py # Logging / save helpers
models/
har.py # HAR, HAR-J, HAR-RS, HARQ, Log-HAR
arfima.py # ARFIMA (long memory)
arma.py # ARMA on log realized volatility
mem.py # Multiplicative error model (Engle, 2002)
foundation.py # TSFM wrappers (Chronos-Bolt, TimesFM, Moirai,
# Moirai-MoE, Lag-Llama, Toto, Sundial, TTM)
forecasting/
rolling_forecast.py # Walk-forward and zero-shot forecast drivers
evaluation/
loss_functions.py # MSE, MAE, QLIKE, R2_OOS
dm_test.py # Diebold-Mariano test
mcs.py # Model Confidence Set
mz_regression.py # Mincer-Zarnowitz regressions
gr_fluctuation.py # Giacomini-Rossi fluctuation test
# Pipeline entry points (run in the order documented below)
run_baselines_volare.py # 1. Econometric baselines
run_foundation_volare.py # 2. TSFM zero-shot forecasts
run_evaluation_volare.py # 3. Metrics, DM tests, MCS
run_advanced_evaluation.py # 4. MZ regressions, Giacomini-Rossi tests
run_robustness.py # 5. MZ bias correction, 252- vs 512-day window
compute_subsample_metrics.py # 6. Pre/post-COVID subsample metrics
process_results.py # 7. LaTeX tables for the paper
generate_figures.py # 8. fig1_forecast_vs_actual, fig2_mcs_heatmap
gen_fig_qlike_boxplot.py # 9. fig_qlike_boxplot
gen_fig_persistence_drivers.py # 10. fig_persistence_drivers
# Helper modules (imported by entry points; do not run directly)
run_baselines.py # Helpers shared with run_baselines_volare.py
run_evaluation.py # Helpers shared with run_evaluation_volare.py
# and run_advanced_evaluation.py
cluster/
*.slurm # SLURM scripts for GPU cluster execution
setup_models.sh # Environment setup for cluster
This repository does not include the underlying data. Realized volatility series are from the VOLARE dataset (VOLatility Archive for Realized Estimates). Download the bulk dataset and place files under data/raw/volare/.
| Econometric | Time Series Foundation Models |
|---|---|
| HAR (Corsi, 2009) | Chronos-Bolt-Small (Amazon) |
| Log-HAR (Corsi, 2009) | Chronos-Bolt-Base (Amazon) |
| HAR-J (Andersen et al., 2007) | Moirai 2.0-Small (Salesforce) |
| HAR-RS (Patton and Sheppard, 2015) | Moirai-MoE-Small (Salesforce) |
| HARQ (Bollerslev et al., 2016) | TimesFM 2.5 (Google) |
| ARFIMA (Granger, 1980) | Toto (Datadog) |
| ARMA (on log RV) | Sundial (Tsinghua University) |
| MEM (Engle, 2002) | Lag-Llama (Rasul et al., 2024) |
| TTM (IBM) |
Log-HAR is the headline econometric benchmark: all relative loss ratios are computed against it.
conda create -n tsfm-rv python=3.11
conda activate tsfm-rv
pip install -r requirements.txtSome TSFMs require a CUDA-capable GPU for inference. Econometric baselines run on CPU.
Run in order:
# Forecasts
python code/run_baselines_volare.py # 1. Econometric baselines (CPU)
python code/run_foundation_volare.py # 2. TSFM zero-shot forecasts (GPU)
# Evaluation
python code/run_evaluation_volare.py # 3. Metrics, DM tests, MCS
python code/run_advanced_evaluation.py # 4. MZ regressions, Giacomini-Rossi tests
python code/run_robustness.py # 5. MZ bias correction, 512-day window
python code/compute_subsample_metrics.py # 6. Pre/post-COVID subsample metrics
# Tables and figures for the paper
python code/process_results.py # 7. Most LaTeX tables in paper/tables/
python code/generate_figures.py # 8. fig1, fig2 in paper/figures/
python code/gen_fig_qlike_boxplot.py # 9. fig_qlike_boxplot
python code/gen_fig_persistence_drivers.py # 10. fig_persistence_driversForecasts and metrics land in results/volare/. LaTeX tables and PDF
figures land in paper/tables/ and paper/figures/.
Three tables in the paper (table_computational_cost.tex,
table_pretraining_data.tex, mz_regression_all.tex) are authored by hand
and are not regenerated by any script.