Abstract

This paper presents theoretical results in 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. * This paper began as a synthesis of at least three UCSD Ph.D. dissertations on various aspects of multivariate ARCH modelling, byYoshi Baba, Dennis Kraft and Ken Kroner. In fact, an early version of this paper was written by Baba, Engle, Kraft and Kroner, which led to the acronym (BEKK) used in this paper for the new parameterization presented. In the interests of continui...

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