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.
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