Spatial-serial dependency in multivariate GARCH models and dynamic copulas: A simulation study

The serial dependency of multivariate nancial data will often be ltered by con-sidering the residuals of univariate GARCH models adapted to every single series.This is the correct ltering strategy if the multivariate process follows a so-calledcopula based multivariate dynamic model (CMD). These multivariate dynamic mo-dels combine univariate GARCH in a linear or nonlinear way. In these models theparameters of the marginal distribution (=univariate GARCH models) and the de-pendence parameter are separable in the sense that they can be estimated in twoor more steps. In the rst step the parameters of the marginal distribution will beestimated and in the second step the parameter(s) of dependence. To the class ofCMD models belong several multivariate GARCH models like the CCC and the DCCmodel. In contrast the BEKK model, f.e., does not belong to this class. If the BEKKmodel is correctly specied the above mentioned ltering strategy could fail from atheoretical point of view. Up to now, it is not known which dynamic copula is incor-porated in a BEKK model. We will show that if the distribution of the innovations(i.e. the residuals) of MGARCH models is spherical the conditional distribution ofthe whole MGARCH process belongs to the elliptical distribution family.[...]