For leverage heterogeneous autoregressive (LHAR) models with jumps and other covariates, called LHARX models, multistep forecasts are derived. Some optimal properties of forecasts in terms of conditional volatilities are discussed, which tells us to model conditional volatility for return but not for the LHARX regression error and other covariates. Forecast standard errors are constructed for which we need to model conditional volatilities both for return and for LHAR regression error and other blue covariates. The proposed methods are well illustrated by forecast analysis for the realized volatilities of the US stock price indexes: the S&P 500, the NASDAQ, the DJIA, and the RUSSELL indexes.
Bibliographical noteFunding Information:
The authors are very thankful for the constructive comments of two referees, which improved the paper substantially. This study was supported by a grant from the National Research Foundation of Korea (2016R1A2B4008780).
© 2018 John Wiley & Sons, Ltd.
- LHARX model
- implied volatility
- realized volatility
- volatility index