MARGINALIZATION AND CONTEMPORANEOUS AGGREGATION IN MULTIVARIATE GARCHPROCESSES

We first of all show that contemporaneous aggregation of independent u nivariate GARCH processes yields a weak GARCH process as introduced by Drost and Nijman (1993). Subsequently we analyze the dependence of th e parameters in the aggregate on the parameters in the underlying mode ls and show that the variance parameters after aggregation depend on t he underlying variance and kurtosis parameters. Then we generalize the results by showing that a linear combination of variables generated b y a multivariate GARCH process will also be weak GARCH. Finally we der ive the marginal (weak GARCH) processes implied by several multivariat e GARCH processes.