The Joint Moment Generating Function of Quadratic Forms in Multivariate Autoregressive Series: The Case with Deterministic Components

22 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: 1996

Abstract

Let {X_{t}} follow a discrete Gaussian Vector Auto-Regression with deterministic components. We derive the exact finite-sample joint Moment Generating Function (MGF) of the quadratic forms that form the basis for the sufficient statistic. The formula is then specialized to the limiting MGF of functionals involving multivariate and univariate Ornstein-Uhlenbeck processes, drifts and time trends. Such processes arise asymptotically from more general non-Gaussian processes as well as the Gaussian {X_{t}}, and have also been used in areas other than time series, such as the 'goodness of fit' literature.

Suggested Citation

Abadir, Karim M. and Larsson, Rolf, The Joint Moment Generating Function of Quadratic Forms in Multivariate Autoregressive Series: The Case with Deterministic Components (1996). Econometric Theory, Vol. 12, p. 682, 1996. Available at SSRN: https://ssrn.com/abstract=1985509

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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