Regime-Gated Residual Mixture-of-Experts for Cross-Sectional Volatility Forecasting

2026-08-12

AI Summary

Financial volatility exhibits state-dependent dynamics, yet directly incorporating market state information into neural networks often leads to training instability. To address this, this work proposes the RG-ResMoE architecture, which innovatively employs state variables solely within a soft routing gate to modulate expert selection—rather than feeding them directly into the prediction pathway—thereby effectively isolating non-stationary influences while maintaining model compactness. Integrating a residual mixture-of-experts mechanism with a rolling forward evaluation framework, the proposed method significantly outperforms capacity-matched MLPs on both U.S. and Japanese equity data, achieving superior predictive accuracy, enhanced training stability, and better Value-at-Risk (VaR) calibration. Moreover, soft routing consistently demonstrates clear advantages over hard routing.

Abstract

Financial volatility is regime dependent, yet incorporating regime information into neural networks can also destabilize training. This paper asks where such information should enter a neural cross-sectional volatility forecasting model. We study five-day realized-volatility forecasts for 1,027 U.S. equities using a rolling walk-forward evaluation framework in which information, model capacity, hyperparameter tuning, and random seeds are matched across architectures. We propose RG-ResMoE, a regime-gated residual mixture-of-experts architecture in which regime information is used only for expert routing rather than for direct forecasting. The base predictor models volatility from stock features, while a gating network uses regime state variables to route residual corrections. RG-ResMoE consistently outperforms a capacity-matched MLP in both forecasting accuracy and training stability in the main U.S. study. Similar gains are observed on an independent Japanese panel. The integration pathway is decisive: appending the same regime variables directly to the forecasting input degrades both predictive performance and training stability, whereas restricting them to the routing gate improves accuracy and Value-at-Risk calibration. Hard routing consistently underperforms soft routing. The results suggest that, in compact neural volatility forecasting models, the primary value of mixture-of-experts models lies less in increasing model capacity than in controlling how nonstationary regime information influences prediction.

Problem

• volatility forecasting
• regime dependence
• mixture-of-experts
• neural networks
• training stability

Innovation

• Mixture-of-Experts
• Regime-Gated Routing
• Volatility Forecasting
• Neural Network Stability
• Cross-Sectional Prediction