THE JOINT MOMENT GENERATING FUNCTION OF QUADRATIC FORMS IN MULTIVARIATE AUTOREGRESSIVE SERIES*

Paper number: 94/04

Year: 1994

Paper Category: Discussion Paper

Authors

Karim M.Abadir
University of Exeter

Rolf Larson
Uppsala University

Abstract

Let {Xt} be a discrete multivariate autoregressive process of order 1. The paper derives the joint moment generating function (mgf) of the two quadratic forms that are used to define statistics relating to the parameters of this process. The formula is then specialized to some cases of interest, including the mgf of functionals of multivariate Ornstein-Uhlenbeck processes.

Keywords and phrases: Vector Autoregressive (VAR) processes, moment generating function (mgf), quadratic forms, functionals of multivariate Wiener and Ornstein-Uhlenbeck processes, systems of ordinary difference equations.

* AMS 1991 subject classifications. Primary 62H10,62M10; secondary 60J60, 60H05, 62E15.