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

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

2007-12-05

arxiv.org/abs/0712.0679v1

The Annals of Statistics (2009) 1-32

Mathematics

Statistics Theory

Scientific paper

Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate or multivariate GARCH, ARCH, ARMA-GARCH processes) the assumptions required for establishing these results are often weaker than existing conditions. The QMLE asymptotic behavior is also given for numerous new examples of univariate or multivariate processes (for instance TARCH or NLARCH processes).

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