Theoretical and evidence-based examination of multiplicative volatility models that decompose the conditional variance into a short- and a long-term component.
We examine the forecast performance of multiplicative volatility models that can be decomposed into a short- and a long-term component. First, we show that in multiplicative models, returns have a higher kurtosis and squared returns have a more persistent autocorrelation function than in the nested GARCH model. Second, we provide theoretical and simulation evidence suggesting that the QLIKE loss should be preferred relative to the squared error loss when comparing volatility forecasts. In a Monte-Carlo simulation, we investigate how the multiplicative structure affects forecast performance both in comparison to the nested GARCH model and the popular HAR model. Finally, we consider an application to S&P 500 returns. Based on the QLIKE loss and forecast horizons of two- to three-months ahead, our results show that multiplicative GARCH models incorporating financial and macroeconomic variables improve upon the HAR model.
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)