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QML ESTIMATION OF A CLASS OF MULTIVARIATE ASYMMETRIC GARCH MODELS

Published online by Cambridge University Press:  03 August 2011

Christian Francq  and
Jean-Michel Zakoïan
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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.

Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 1 , February 2012 , pp. 179 - 206
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

The authors sincerely thank the editor Peter C.B. Phillips, the co-editor Pentti Saikkonen, and two anonymous referees for their very helpful comments and suggestions.

References

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