  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.
