Stock index realized volatility forecasting in the presence of heterogeneous leverage effects and long range dependence in the volatility of realized volatility

In this article, we account for the presence of heterogeneous leverage effects and the persistence in the volatility of stock index realized volatility. The Heterogeneous Autoregressive (HAR) realized volatility model is extended in order to account for asymmetric responses to negative and positive shocks occurring at distinct frequencies, as well as, for the long range dependence in the heteroscedastic variance of the residuals. Compared with established HAR and Autoregressive Fractionally Integrated Moving Average (ARFIMA) realized volatility models, the proposed model exhibits superior in-sample fitting, as well as, out-of-sample volatility forecasting performance. The latter is further improved when the realized power variation is used as a regressor, while we show that our analysis is also robust against microstructure noise.