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We suggest the Doubly Multiplicative Error class of models (DMEM) formodeling and forecasting realized volatility, which combines two componentsaccommodating low-, respectively, high-frequency features in the data. Wederive the theoretical properties of the Maximum Likelihood and GeneralizedMethod of Moments estimators. Two such models are then proposed, theComponent-MEM, which uses daily data for both components, and the MEM-MIDAS,which exploits the logic of MIxed-DAta Sampling (MIDAS). The empiricalapplication involves the S&P 500, NASDAQ, FTSE 100 and Hang Seng indices:irrespective of the market, both DMEM's outperform the HAR and other relevantGARCH-type models.

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