# Two are better than one: volatility forecasting using multiplicative component GARCH-MIDAS models

### Abstract

Theoretical and evidence-based examination of multiplicative volatility models that decompose the conditional variance into a short- and a long-term component.

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We examine the properties and forecast performance of multiplicative volatility models that can be decomposed into a short- and a long-term component. Our leading example for such a model is the GARCH-MIDAS of Engle et al. (2013). We derive certain properties of multiplicative volatility models such as the kurtosis of returns, the autocorrelation function of squared returns, the R^2 of a Mincer-Zarnowitz regression and evaluate these models in a Monte-Carlo simulation. Most importantly, 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. For S&P 500 data, our results show that the GARCH-MIDAS based on housing starts as 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)