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

The Case with Deterministic Components

Published online by Cambridge University Press:  07 February 2001

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

Let {Xt} follow a discrete Gaussian vector autoregression 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 and also from the Gaussian {Xt} and have also been used in areas other than time series, such as the “goodness of fit” literature.

Type
Research Article
Information
Econometric Theory , Volume 17 , Issue 1 , February 2001 , pp. 222 - 246
Copyright
© 2001 Cambridge University Press

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