QML estimation of a class of multivariate asymmetric GARCH models

We establish the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameters of a class of multivariate asymmetric generalized autoregressive conditionally heteroskedastic processes, allowing for cross leverage effects. The conditions required to establish the asymptotic properties of the QMLE are mild and coincide with the minimal ones in the univariate case. In particular, no moment assumption is made on the observed process. Instead, we require strict stationarity, for which a necessary and sufficient condition is established. The asymptotic results are illustrated by Monte Carlo experiments, and an application to a bivariate exchange rates series is proposed.