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

A comprehensive comparison of the volatility predictive abilities of different classes of time-varying volatility models is considered. The models include the exponential GARCH (EGARCH) and stochastic volatility (SV) models using daily returns, the heterogeneous autoregressive (HAR) model using daily realized volatility (RV) and the realized EGARCH (REGARCH) and realized SV (RSV) models using both. All the models are extended to accommodate the well-known phenomenon in stock markets of a negative correlation between today’s return and tomorrow’s volatility. The HAR model is estimated by the ordinary least squares method, while the EGARCH and REGARCH models are estimated by the quasi-maximum likelihood method. Since it is not straightforward to evaluate the likelihood of the SV and RSV models, a Bayesian estimation via Markov chain Monte Carlo is employed. The models are applied to daily returns and/or RVs of four stock indices: the Dow Jones Industrial Average, the Nikkei 225, the Financial Times Stock Exchange 100, and the Euro Stoxx 50. By conducting predictive ability tests and analyses based on model confidence sets, it is confirmed that the models that use RV (RSV, REGARCH, and RSV) outperform those that do not (EGARCH and SV); this suggests that RV provides useful information in forecasting volatility. Moreover, it is found that the RSV model performs better than the HAR and REGARCH models.