DeepHAR: Heterogeneous attention-conditioned regression network for realized volatility forecasting

Accurate volatility forecasting is essential for risk management and portfolio allocation; yet existing methods face key limitations. Linear Heterogeneous Autoregressive (HAR)-type econometric models lack adaptability to regime shifts, while general-purpose deep learning models fail to capture volatility-specific structures, often underperforming compared to simple linear benchmarks. We propose DeepHAR, a heterogeneous attention-based regression framework that embeds the Heterogeneous Market Hypothesis (HMH) into a neural architecture for realized volatility forecasting. DeepHAR constructs horizon-specific representations via temporal attention pooling and models asymmetric cross-horizon dependencies through heterogeneous cross-attention, conditioning short-term volatility shocks on mid- and long-term market memory. A dual-path decomposition further separates this representation into trend and shock components, capturing volatility persistence and mean reversion. Experiments on major U.S. equity index ETFs over 2005–2025 show that DeepHAR achieves the best overall forecasting performance, with statistically significant error reductions confirmed by Diebold–Mariano tests. Under extreme stress, DeepHAR achieves the lowest MSE in high-volatility regimes and leads across markets during the 2025 Tariff Shock, while remaining the strongest nonlinear forecaster during the COVID-19 crash, though a simpler benchmark attains marginally lower MSE in this period. Attention-based analyses show cross-horizon reallocation that intensifies under severe shocks such as COVID-19, consistent with the HMH, while utility-based evaluations confirm that forecasting gains translate into tangible portfolio benefits. These findings indicate that embedding domain-specific market structure into attention mechanisms offers a more effective path toward robust, interpretable volatility forecasting than purely linear or purely generic deep learning approaches.