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ASYMPTOTIC THEORY FOR A VECTOR ARMA-GARCH MODEL

Published online by Cambridge University Press:  31 January 2003

Shiqing Ling  and
Michael McAleer
Shiqing Ling
Affiliation:
Hong Kong University of Science and Technology
Michael McAleer
Affiliation:
University of Western Australia
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Abstract

This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) model. The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established. Consistency of the quasi-maximum-likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate autoregressive conditional heteroskedasticity (ARCH) and GARCH models. Moreover, the asymptotic normality of the QMLE for the vector ARCH model is obtained under only the second-order moment of the unconditional errors and the finite fourth-order moment of the conditional errors. Under additional moment conditions, the asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH models and also a consistent estimator of the asymptotic covariance.The authors thank the co-Editor, Bruce Hansen, and two referees for very helpful comments and suggestions and acknowledge the financial support of the Australian Research Council.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 2 , April 2003 , pp. 280 - 310
Copyright
© 2003 Cambridge University Press

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