QML ESTIMATION OF A CLASS OF MULTIVARIATE ASYMMETRIC GARCH MODELS

Christian Francq () and Jean-Michel Zakoïan
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Christian Francq: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, IP Paris - Institut Polytechnique de Paris
Jean-Michel Zakoïan: LFA - Laboratoire de Finance Assurance - Centre de Recherche en Économie et Statistique (CREST) - GENES - Groupe des Écoles Nationales d'Économie et Statistique, EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie - Université de Lille, Sciences et Technologies - Université de Lille, Sciences Humaines et Sociales - PRES Université Lille Nord de France - Université de Lille, Droit et Santé

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Abstract: We establish the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameters of a class of multivariate asymmetric generalized autoregressive conditionally heteroskedastic processes, allowing for cross leverage effects. The conditions required to establish the asymptotic properties of the QMLE are mild and coincide with the minimal ones in the univariate case. In particular, no moment assumption is made on the observed process. Instead, we require strict stationarity, for which a necessary and sufficient condition is established. The asymptotic results are illustrated by Monte Carlo experiments, and an application to a bivariate exchange rates series is proposed.

Date: 2011-08-03
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Published in Econometric Theory, 2011, 28 (1), pp.179-206. ⟨10.1017/S0266466611000156⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05417552

DOI: 10.1017/S0266466611000156

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