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

28 Pages Posted: 15 Jan 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Rolf Larsson

Stockholm University

Date Written: May 12, 1996

Abstract

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

Suggested Citation

Abadir, Karim M. and Larsson, Rolf, The Joint Moment Generating Function of Quadratic Forms in Multivariate Autoregressive Series (May 12, 1996). Econometric Theory, Vol. 17, p. 222, 2001. Available at SSRN: https://ssrn.com/abstract=1985482

Karim M. Abadir (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

Rolf Larsson

Stockholm University ( email )

Department of Statistics
S-106 91 Stockholm
Sweden

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