Memory, Roughness, and Information Persistence in Financial Markets: A Structural Approach to Volatility Forecasting

2026-05-22

AI Summary

This study addresses the challenge of improving volatility forecasting in financial markets by integrating long memory, rough volatility, and information persistence. The proposed framework combines semi-parametric long-memory estimation—employing both Geweke–Porter–Hudak and local Whittle methods—with rough volatility diagnostics and a structured HAR-X regression model. Notably, it introduces cross-sectional and industry-level persistence aggregation measures and their interactions with market stress regimes for the first time. Empirical validation across 115 S&P 500 constituents demonstrates significant out-of-sample predictive gains, particularly in long-horizon forecasts and volatility-managed portfolios. These results indicate that volatility persistence conveys incremental economic information beyond conventional risk factors.

Abstract

This paper studies the joint role of long-memory dynamics,rough-volatility behavior, and persistence-based forecasting features in equity volatility modeling. We combine semiparametric long-memory estimation, rough-volatility diagnostics, and structured forecasting regressions to examine whether persistence measures contain economically meaningful forecasting information beyond conventional volatility predictors. Using a panel of 115 S&P500 constituents from November 2001 through April 2026, we document that volatility proxies exhibit substantial long-memory behavior and locally rough dynamics. The cross-sectional mean Geweke-Porter-Hudak estimate of the memory parameter is $\hat{d} = 0.226$, while the corresponding local-Whittle estimate is $\hat{d} = 0.440$, with statistical significance observed across nearly the entire panel. Rolling estimates of persistence rise substantially during the global financial crisis and the COVID period and display a positive contemporaneous association with the VIX. We then examine whether persistence-related features improve out-of-sample volatility forecasts beyond standard HAR and HAR-X benchmarks. Incorporating cross-sectional persistence aggregates, sectoral persistence measures, and persistence-by-stress interaction terms produces moderate but statistically significant forecasting improvements, particularly at longer horizons and during stress regimes. Forecast gains are strongest during periods of elevated market volatility and in volatility-managed portfolio applications. The results suggest that persistence measures may serve as useful reduced-form indicators of the duration and propagation of uncertainty in financial markets, although the paper does not claim structural identification of the economic mechanisms generating persistence.

Problem

• long-memory
• rough volatility
• persistence
• volatility forecasting
• financial markets

Innovation

• long-memory
• rough volatility
• persistence forecasting
• structured regression
• volatility prediction