We examine the properties and forecast performance of multiplicative volatility specifications that belong to the class of GARCH-MIDAS models suggested in Engle et al.~(2013). In those models volatility is decomposed into a short-term GARCH component and a long-term component that is driven by an explanatory variable. We derive the kurtosis of returns, the autocorrelation function of squared returns, and the $R^2$ of a Mincer-Zarnowitz regression and evaluate these models in a Monte-Carlo simulation. For S&P 500 data, we compare the forecast performance of GARCH-MIDAS models with a wide range of competitor models such as HAR, Realized GARCH, HEAVY and Markov-Switching GARCH. Our results show that the GARCH-MIDAS based on housing starts as an explanatory variable significantly outperforms all competitor models at forecast horizons of two and three months ahead.
A preliminary version of this paper circulated unter the title “On the Statistical Properties of Multiplicative GARCH Models” (University of Heidelberg, Department of Economics, Discussion Paper No. 613, see https://www.uni-heidelberg.de/md/awi/forschung/dp613.pdf)