发表机构
Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨路径签名何时改进波动率区间预测，发现其在美国市场提升HAR模型准确率2.7个百分点，尤其在均值回复速度差异时有效，但未带来夏普比率增益。
AI 中文摘要
我们研究了路径签名——作为收益路径的无模型特征日益常用——何时能改进波动率区间的样本外预测。在2005年至2025年的美国及发达市场日度股票收益中，机器学习分类器未能超越已实现波动率的异质自回归（HAR）回归，尽管签名在美国提高了分类器的准确性和概率预测。将原始签名加入HAR回归本身，能改进美国下月波动率三分位数的预测，使平衡准确率提高2.7个百分点，并在多重检验校正后降低排序概率得分，而加入传统波动率特征则无此效果；在美国以外，没有任何增益在校正后幸存。受控的Heston实验解释了这一模式：当区间在方差水平上不同时（已实现波动率已捕捉到），签名带来的增益有限；而当区间共享同一平稳方差法则但均值回复速度不同时，签名带来的增益更大。然而，更好的区间识别并未带来更早的区间变化信号，且没有准确率增益转化为波动率管理投资组合中显著的夏普比率增益。因此，签名增加了关于波动率如何演变的信息，而这是已实现波动率预测因子所遗漏的。
英文摘要
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.
