August 2025
(Revised September 2026)
Linear and Nonlinear Econometric Models versus Machine-Learning Models: Evidence from Realized-Volatility Forecasting
Rehim Kilic
Abstract:
This paper examines which representations of persistence and nonlinearity are most useful for forecasting realized volatility and whether machine learning adds value beyond econometric models designed for long memory and regime dependence. We compare HAR, ARFIMA, threshold HAR, smooth-transition HAR, and Markov-switching HAR with XGBoost and several neural-network models for the S&P 500 and 40 U.S. equities. Models are evaluated under a baseline information set using realized-volatility history and an extended set of predictors selected by Elastic Net. Forecast performance is assessed using MSFE, MAE, QLIKE, Model Confidence Sets, Diebold–Mariano tests, realized utility, and filtered-historical-simulation VaR and expected shortfall. The results reveal a robust horizon-dependent ranking: Markov-switching HAR performs best at short horizons, ARFIMA generally leads at the monthly horizon, and the five-day horizon is intermediate. Machine-learning models sometimes improve on HAR but do not systematically outperform the broader econometric set. These findings are robust across estimation windows, re-estimation frequencies, richer information sets, log-volatility targets, and individual equities; stock-level results are also robust to an alternative realized-volatility measure. Overall, forecast performance depends primarily on capturing the persistence and nonlinear dynamics most relevant at each horizon.
Keywords: Realized volatility, machine learning, HAR, ARFIMA, Markov switching, long memory, volatility forecasting
DOI: https://doi.org/10.17016/FEDS.2025.061r1
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September 02, 2026
