We propose a general GARCH framework that allows the 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 the volatility dynamics are driven by what we...

We estimate MIDAS regressions with various (bi)power variations to predict future volatility measured via increments in quadratic variation. Instead of pre-determining the (bi)power variation we parameterize it and estimate the intra-daily return power transformation that optimally predicts...