Forecasting realized volatility: Does anything beat linear models?

We evaluate the performance of several linear and nonlinear machine learning (ML) models in forecasting the realized volatility (RV) of ten global stock market indices in the period from January 2000 to December 2021. We train models using a dataset that includes past values of the RV and additional predictors, including lagged returns, implied volatility, macroeconomic and sentiment variables. We compare these models to widely used heterogeneous autoregressive (HAR) models. Our main conclusions are that (i) the additional predictors improve the out-of-sample forecasts at the daily and weekly forecast horizons; (ii) we find no evidence that nonlinear ML models can statistically outperform linear models in general; and (iii) in terms of the economic value that an investor would derive from monthly RV forecasts to build volatility-timing portfolios, simpler models without additional predictors work better.