美联储-线性与非线性计量经济学模型与机器学习模型的对比：已实现波动率预测（英）

Finance and Economics Discussion SeriesFederal Reserve Board, Washington, D.C.ISSN 1936-2854 (Print)ISSN 2767-3898 (Online)Linear and nonlinear econometric models against machinelearning models: realized volatility predictionRehim Kilic2025-061Please cite this paper as:Kilic, Rehim (2025).“Linear and nonlinear econometric models against machine learn-ing models:realized volatility prediction,”Finance and Economics Discussion Se-ries 2025-061.Washington:Board of Governors of the Federal Reserve System,https://doi.org/10.17016/FEDS.2025.061.NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminarymaterials circulated to stimulate discussion and critical comment. The analysis and conclusions set forthare those of the authors and do not indicate concurrence by other members of the research staff or theBoard of Governors. References in publications to the Finance and Economics Discussion Series (other thanacknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.Linear and nonlinear econometric models against machinelearning models: realized volatility predictionRehim Kılı¸c∗July 2025AbstractThis paper fills an important gap in the volatility forecasting literature by comparinga broad suite of machine learning (ML) methods with both linear and nonlinear econo-metric models using high-frequency realized volatility (RV) data for the S&P 500.Weevaluate ARFIMA, HAR, regime-switching HAR models (THAR, STHAR, MSHAR), andML methods including Extreme Gradient Boosting, deep feed-forward neural networks, andrecurrent networks (BRNN, LSTM, LSTM-A, GRU). Using rolling forecasts from 2006 on-ward, we find that regime-switching models—particularly THAR and STHAR—consistentlyoutperform ML and linear models, especially when predictors are limited. These modelsalso deliver more accurate risk forecasts and higher realized utility. While ML models cap-ture some nonlinear patterns, they offer no consistent advantage over simpler, interpretablealternatives. Our findings highlight the importance of modeling regime changes throughtransparent econometric tools, especially in real-world applications where predictor avail-ability is sparse and model interpretability is critical for risk management and portfolioallocation.JEL Classification: C10, C50, G11, G15.Keywords: Realized volatility, machine learning, regime-switching, nonlinearity, VaR, fore-casting.∗Federal Reserve Board, Washington, DC E-mail: rehim.kilic@frb.gov. The views presented in this paperare solely those of the author and do not represent those of the Board of Governors or any entities connected tothe Federal Reserve System.1IntroductionAccurate volatility forecasting is vital for assessing systemic risk, asset pricing, portfolio allo-cation, and risk management. Since the foundational work of Engle (1982), Bollerslev (1986),and Taylor (1982), volatility modeling has evolved significantly but remains a challenging task,as dis