The HARX-GJR-GARCH skewed-t multipower realized volatility modelling for S&P 500

The heterogeneous autoregressive (HAR) models are used in modeling high frequency multipower realized volatility of the S&P 500 index. Extended from the standard realized volatility, the multipower realized volatility representations have the advantage of handling the possible abrupt jumps by smoothing the consecutive volatility. In order to accommodate clustering volatility and asymmetric of multipower realized volatility, the HAR model is extended by the threshold autoregressive conditional heteroscedastic (GJR-GARCH) component. In addition, the innovations of the multipower realized volatility are characterized by the skewed student-t distributions. The extended model provides the best performing in-sample and out-of-sample forecast evaluations