Hitotsubashi Institute for Advanced Study


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 the stochastic 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 Average (DJIA) in US and Nikkei 225 (N225) in Japan. All models are extended to accommodate the well-known phenomenon in stock markets of a negative correlation between today’s return and tomorrow’s volatility. We estimate the HAR model by the ordinary least squares (OLS) and the EGARCH and REGARCH models by the quasi-maximum likelihood (QML) method. Since it is not straightforward to evaluate the likelihood of the SV and RSV models, we apply a Bayesian estimation via Markov chain Monte Carlo (MCMC) to them. By conducting predictive ability tests and analyses based on model confidence sets, we confirm that the models using 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. The cumulative loss analysis suggests that the differences of the predictive abilities among the models are partly caused by the rise of volatility.

Report No.: HIAS-E-104
Author(s): Makoto Takahashi(a)
Toshiaki Watanabe(b)
Yasuhiro Omori(c)
Affiliation: (a) Faculty of Business Administration, Hosei University
(b) Institute of Economic Research, Hitotsubashi University
(c) Faculty of Economics, University of Tokyo
Issued Date: January, 2021
Keywords: Exponential GARCH (EGARCH) model; Heterogeneous autoregressive (HAR) model; Markov chain Monte Carlo (MCMC); Realized volatility; Stochastic volatility; Volatility forecasting
JEL: C11, C22, C53, C58, G17