Multivariate ARCH models.

Summary We study the convergence in probability of the maximum likelihood estimator of an ARMA model whose errors follow a GARCH (1, 1) process according to the specification of Baba, Engle, Kraft and Kroner. We establish conditions for the existence of moments of order greater than two. The conditions of strict stationarity and ergodicity of some constrained models are presented. Finally, we propose a general framework for the continuous time approximation of multivariate ARCH models.