Forecasting Stock Index Realized Volatility with an Asymmetric HAR-FIGARCH Model: The Case of S&P 500 and DJI Stock Indices

Abstract

The approximate long memory Heterogeneous Autoregressive (HAR) model proposed by Corsi is extended in order to account for leverage effects in the realized volatility process and the long memory of the conditional variance of the HAR residuals. The proposed model is estimated using ten years of S&P 500 and DJIA indices intraday data, revealing a heterogeneous component structure in asymmetric effects and a statistically significant long memory property in the “volatility of realized volatility”. Compared with established HAR and ARFIMA realized volatility models, the proposed model exhibits superior in-sample fitting, as well as out-of-sample day-ahead realized volatility forecasting performance. On a day-ahead Value at Risk (VaR) application, the proposed model outperforms all of its competitors when the opportunity cost of the reserved capital is taken into account, satisfying also Christoffersen’s conditional coverage test criteria for the DJIA index.