Abstract: We propose a general GARCH framework that allows one to predict volatility using returns sampled at a higher frequency than the prediction horizon. We call the class of models High FrequencY Data-Based PRojectIon-Driven GARCH, or HYBRID-GARCH models, as volatility dynamics are driven by what we call HYBRID processes. The HYBRID processes can involve data sampled at any frequency. We study the theoretical properties as well as statistical inference. An application reports the superior out-of-sample forecasting performance of the new class of models, including the time of the recent financial crisis.

Key words and phrases: Filtering, GARCH jump diffusion, HYBRID process, realized measure, temporal aggregation, weak GARCH.