%0 Generic
%A Conrad, Christian
%A Kleen, Onno
%C Heidelberg
%D 2016
%F heidok:20486
%K Forecast evaluation, GARCH-MIDAS, Mincer-Zarnowitz regression,  volatility persistence, volatility component model, long-term volatility.
%R 10.11588/heidok.00020486
%T On the statistical properties of multiplicative GARCH models
%U https://archiv.ub.uni-heidelberg.de/volltextserver/20486/
%V 0613
%X We examine the statistical properties of multiplicative GARCH models. First, we show that in multiplicative models, returns have higher kurtosis and squared returns have a more persistent autocorrelation function than in the nested GARCH model. Second, we extend the results of Andersen and Bollerslev (1998) on the upper bound of the R2 in a Mincer-Zarnowitz regression to the case of a multiplicative GARCH model, using squared returns as a proxy for the true but unobservable conditional variance. Our theoretical results imply that multiplicative GARCH models provide an explanation for stylized facts that cannot be captured by classical GARCH modeling.