Capturing volatility persistence: a dynamically complete realized EGARCH-MIDAS model

We introduce extensions of the Realized Exponential GARCH model (REGARCH) that capture the evident high persistence typically observed in measures of financial market volatility in a tractable fashion. The extensions decompose conditional variance into a short-term and a long-term component. The latter utilizes mixed-data sampling or a heterogeneous autoregressive structure, avoiding parameter proliferation otherwise incurred by using the classical ARMA structures embedded in the REGARCH. The proposed models are dynamically complete, facilitating multi-period forecasting. A thorough empirical investigation with an exchange-traded fund that tracks the S&P500 Index and 20 individual stocks shows that our models better capture the dependency structure of volatility. This leads to substantial improvements in empirical fit and predictive ability at both short and long horizons relative to the original REGARCH. A volatility-timing trading strategy shows that capturing volatility persistence yields substantial utility gains for a mean–variance investor at longer investment horizons.