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Multivariate Simultaneous Generalized ARCH

Published online by Cambridge University Press:  11 February 2009

Robert F. Engle  and
Kenneth F. Kroner
Robert F. Engle
Affiliation:
University of California, San Diego
Kenneth F. Kroner
Affiliation:
University of Arizona
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Abstract

This paper presents theoretical results on the formulation and estimation of multivariate generalized ARCH models within simultaneous equations systems. A new parameterization of the multivariate ARCH process is proposed, and equivalence relations are discussed for the various ARCH parameterizations. Constraints sufficient to guarantee the positive definiteness of the conditional covariance matrices are developed, and necessary and sufficient conditions for covariance stationarity are presented. Identification and maximum likelihood estimation of the parameters in the simultaneous equations context are also covered.

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Type
Articles
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Econometric Theory , Volume 11 , Issue 1 , February 1995 , pp. 122 - 150
Copyright
Copyright © Cambridge University Press 1995

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