National University of Kaohsiung;National University of Kaohsiung
This paper uses the Mixed Data Sampling (MIDAS) and the Rolling Window (RW) methods to introduce conditional volatility into the CARR-family models. An augmented CARR model is shown to exhibit the advantages of both range-based volatility and high-frequency data in superior forecasting ability of volatility as compared to the GARCH models. Specifically, using the S&P500 stock index data, we find that the augmented CARR models (MIDAS-CARR and RW-CARR) are increasing the goodness of fit of the models and performing better in in-sample forecasting capability as compared to the GARCH and CARR models. This conclusion holds even with the existence of a structural change on the volatility. The augmented CARR models are also tested for out-of-sample forecasting ability, evaluated with RMSE and MAE statistics. We find that the CARR model is performing better than the GARCH model, and the MIDAS-CARR model and RW-CARR model are also performing better than the CARR model.