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The Joint Moment Generating Function of Quadratic Forms in Multivariate Autoregressive Series

Published online by Cambridge University Press:  11 February 2009

Karim M. Abadir and
Rolf Larsson
Karim M. Abadir
Affiliation:
University of York
Rolf Larsson
Affiliation:
Stockholm University
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Abstract

Let (X1) be a discrete multivariate Gaussian autoregressive process of order 1. The paper derives the exact finite-sample joint moment generating function (m.g.f.) of the three quadratic forms constituting the sufficient statistic of the process. The formula is then specialized to some cases of interest, including the m.g.f. of functional of multivariate Ornstein-Uhlenbeck processes that arise asymptotically from more general (X1) processes as well.

Information

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 4 , October 1996, pp. 682 - 704
Copyright
Copyright © Cambridge University Press 1996

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