On the Weak Consistency of the Quasi-Maximum Likelihood Estimator in VAR Models with BEKK-GARCH(1,q) Errors

Abstract

We provide conditions that enable to prove the weak consistency of the quasi maximum likelihood estimator of the parameters of a vector autoregressive model with GARCH(l,q) errors. The BEKK representation of Engle and Kroner (1995) is used t.o parametrize the multivariate GARCH process.