Doubly Multiplicative Error Models with Long– and Short–run Components

We suggest the Doubly Multiplicative Error class of models (DMEM) for modeling and forecasting realized volatility, which combines two components accommodating low–, respectively, high–frequency features in the data. We derive the theoretical properties of the Maximum Likelihood and Generalized Method of Moments estimators. Two such models are then proposed, the Component-MEM, which uses daily data for both components, and the MEM-MIDAS, which exploits the logic of MIxed–DAta Sampling (MIDAS). The empirical application involves the S&P 500, NASDAQ, FTSE 100 and Hang Seng indices: irrespective of the market, both DMEM’s outperform the HAR and other relevant GARCH–type models.