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Asymptotic Normality of the Quasi-Maximum Likelihood Estimator for Multidimensional Causal Processes

Jean-Marc Bardet and Olivier Wintenberger
The Annals of Statistics
Vol. 37, No. 5B (Oct., 2009), pp. 2730-2759
Stable URL: http://www.jstor.org/stable/30243726
Page Count: 30
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Asymptotic Normality of the Quasi-Maximum Likelihood Estimator for Multidimensional Causal Processes
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Abstract

Strong consistency and asymptotic normality of the quasi-maximum likelihood estimator are given for a general class of multidimensional causal processes. For particular cases already studied in the literature [for instance univariate or multivariate ARCH(∞) 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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