Forecasting Daily Volatility of Stock Price Index Using Daily Returns and Realized Volatility

This paper compares the volatility predictive abilities of some time-varying volatility models such as thestochastic volatility (SV) and exponential GARCH (EGARCH) models using daily returns, the heterogeneous au-toregressive (HAR) model using daily realized volatility (RV) and the realized SV (RSV) and realized EGARCH(REGARCH) models using the both. The data are the daily return and RV of Dow Jones Industrial Aver-age (DJIA) in US and Nikkei 225 (N225) in Japan. All models are extended to accommodate the well-knownphenomenon in stock markets of a negative correlation between today's return and tomorrow's volatility. Weestimate the HAR model by the ordinary least squares (OLS) and the EGARCH and REGARCH models bythe quasi-maximum likelihood (QML) method. Since it is not straightforward to evaluate the likelihood of theSV and RSV models, we apply a Bayesian estimation via Markov chain Monte Carlo (MCMC) to them. Byconducting predictive ability tests and analyses based on model confidence sets, we confirm that the models us-ing RV outperform the models without RV, that is, the RV provides useful information on forecasting volatility.Moreover, we find that the realized SV model performs best and the HAR model can compete with it. Thecumulative loss analysis suggests that the differences of the predictive abilities among the models are partlycaused by the rise of volatility.