Scale or speed? When do path signatures improve volatility-regime forecasts?
Abstract
We study when path signatures, increasingly used as model-free features of return paths, improve out-of-sample forecasts of volatility regimes. In daily United States and developed-market equity returns from 2005 to 2025, machine-learning classifiers do not beat a heterogeneous autoregressive (HAR) regression of realized volatility, although signatures improve the classifiers' accuracy and probability forecasts in the United States. Adding raw signatures to the HAR regression itself improves United States forecasts of next-month volatility terciles, raising balanced accuracy by 2.7 percentage points and lowering the ranked probability score after multiple-testing correction, whereas adding conventional volatility features does not; outside the United States no gain survives correction. Controlled Heston experiments explain the pattern: signatures add modestly when regimes differ in variance level, which realized volatility already captures, and more when regimes share one stationary variance law but differ in mean-reversion speed. Better regime identification does not, however, deliver earlier regime-change signals, and no accuracy gain translates into a resolved Sharpe-ratio gain in a volatility-managed portfolio. Signatures thus add information about how volatility evolves, which realized-volatility predictors miss.
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BibTeX
@misc{lyu2026scale,
title = {{Scale or speed? When do path signatures improve volatility-regime forecasts?}},
author = {Yang Lyu and Kiseop Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06690},
eprint = {2610.06690},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06690},
}
RIS
TY - UNPB
TI - Scale or speed? When do path signatures improve volatility-regime forecasts?
AU - Yang Lyu
AU - Kiseop Lee
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06690
UR - https://arxiv.org/abs/2610.06690
AB - We study when path signatures, increasingly used as model-free features of return paths, improve out-of-sample forecasts of volatility regimes. In daily United States and developed-market equity returns from 2005 to 2025, machine-learning classifiers do not beat a heterogeneous autoregressive (HAR) regression of realized volatility, although signatures improve the classifiers' accuracy and probability forecasts in the United States. Adding raw signatures to the HAR regression itself improves United States forecasts of next-month volatility terciles, raising balanced accuracy by 2.7 percentage points and lowering the ranked probability score after multiple-testing correction, whereas adding conventional volatility features does not; outside the United States no gain survives correction. Controlled Heston experiments explain the pattern: signatures add modestly when regimes differ in variance level, which realized volatility already captures, and more when regimes share one stationary variance law but differ in mean-reversion speed. Better regime identification does not, however, deliver earlier regime-change signals, and no accuracy gain translates into a resolved Sharpe-ratio gain in a volatility-managed portfolio. Signatures thus add information about how volatility evolves, which realized-volatility predictors miss.
ER -