Forecasting stock market volatility: an asymmetric conditional autoregressive range mixed data sampling (ACARR-MIDAS) model

In this paper we extend the conditional autoregressive range (CARR) model to the asymmetric CARR mixed data sampling (ACARR-MIDAS) model, which takes into consideration volatility asymmetry as well as volatility persistence to model and forecast volatility (as measured by price range). The ACARR-MIDAS model multiplicatively decomposes the conditional range into short- and long-term components, where the short-term component is governed by a first-order generalized autoregressive conditional heteroscedasticity-like (GARCH(1,1)-like) process and where it incorporates the lagged return to capture the asymmetric impact of positive and negative returns on volatility, and where the long-term component is specified by smoothing the realized volatility measure in a MIDAS framework. We apply the ACARR-MIDAS model to four international stock market indexes. The empirical results show that the ACARR-MIDAS model significantly outperforms the CARR, ACARR and CARR-MIDAS models in terms of out-of-sample forecasting. Moreover, the superior forecasting ability of the ACARR-MIDAS model is robust to alternative forecasting windows, the realized volatility measure and return-based benchmark models (exponential GARCH-MIDAS and realized exponential GARCH).