Variance targeting estimation of multivariate GARCH models

We establish the strong consistency and the asymptotic normality (CAN) of the variance-targeting estimator (VTE) of the parameters of the multivariate CCC-GARCH(p,q) processes. This method alleviates the numerical difficulties encountered in themaximization of the quasi-likelihood by using an estimator of the unconditional variance.It is shown that the distribution of the VTE can be consistently estimated by asimple residual bootstrap technique. We also use the VTE for testing the model adequacy.A test statistic in the spirit of the score test is constructed, and its asymptoticproperties are derived under the null assumption that the model is well specified.An extension of the VT method to asymmetric CCC-GARCH models incorporatingleverage effects is studied. Numerical illustrations are provided and an empirical applicationbased on daily exchange rates is proposed.