On the statistical properties of multiplicative GARCH models

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.