The Annals of Statistics

Asymptotic normality of the quasi-maximum likelihood estimator for multidimensional causal processes

Jean-Marc Bardet and Olivier Wintenberger

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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).

Article information

Ann. Statist., Volume 37, Number 5B (2009), 2730-2759.

First available in Project Euclid: 17 July 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62F12: Asymptotic properties of estimators

Quasi-maximum likelihood estimator strong consistency asymptotic normality multidimensional causal processes multivariate ARMA–GARCH processes


Bardet, Jean-Marc; Wintenberger, Olivier. Asymptotic normality of the quasi-maximum likelihood estimator for multidimensional causal processes. Ann. Statist. 37 (2009), no. 5B, 2730--2759. doi:10.1214/08-AOS674.

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