Incorporating overnight and intraday returns into multivariate GARCH volatility models

We propose and evaluate mixed-frequency multivariate GARCH models for forecasting low-frequency (weekly) volatility based on high-frequency intraday returns (at 5-minute intervals) and on the overnight returns. The low-frequency conditional volatility matrix is modeled as a weighted sum of an intraday and an overnight component. The components are specified as multivariate GARCH processes of the BEKK type, adapted to the mixed-frequency data setting, and may enter the model as two separate components or as a single one. The models may further be extended by a nonparametrically estimated slowly-varying long-run volatility matrix. We evaluate the models in and out of sample using the 5-minute and overnight returns on four DJIA stocks (AXP, GE, HD, and IBM) from January 1988 to November 2014 and find that they systematically dominate a variety of models that only use lower-frequency data (weekly, daily, or close-to-open and open-to-close returns).