Linear and nonlinear econometric models against machine learning models: realized volatility prediction

This paper fills an important gap in the volatility forecasting literature by comparing a broad suite of machine learning (ML) methods with both linear and nonlinear econometric models using high-frequency realized volatility (RV) data for the S\&P 500. We evaluate ARFIMA, HAR, regime-switching HAR models (THAR, STHAR, MSHAR), and ML methods including Extreme Gradient Boosting, deep feed-forward neural networks, and recurrent networks (BRNN, LSTM, LSTM-A, GRU). Using rolling forecasts from 2006 onward, we find that regime-switching models—particularly THAR and STHAR—consistently outperform ML and linear models, especially when predictors are limited. These models also deliver more accurate risk forecasts and higher realized utility. While ML models capture some nonlinear patterns, they offer no consistent advantage over simpler, interpretable alternatives. Our findings highlight the importance of modeling regime changes through transparent econometric tools, especially in real-world applications where predictor availability is sparse and model interpretability is critical for risk management and portfolio allocation.