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Strong consistency and asymptotic normality of the Quasi-Maximum LikelihoodEstimator (QMLE) are given for a general class of multidimensional causalprocesses. For particular cases already studied in the literature (for instanceunivariate or multivariate GARCH, ARCH, ARMA-GARCH processes) the assumptionsrequired for establishing these results are often weaker than existingconditions. The QMLE asymptotic behavior is also given for numerous newexamples of univariate or multivariate processes (for instance TARCH or NLARCHprocesses).

Asymptotic normality of the Quasi Maximum Likelihood Estimator for multidimensional causal processes