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THE JOINT MOMENT GENERATING FUNCTION OF QUADRATIC FORMS IN MULTIVARIATE AUTOREGRESSIVE SERIES: The Case with Deterministic Components

  • Karim M. Abadir (a1) and Rolf Larsson (a2)
  • Published online: 01 February 2001
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.

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Corresponding author
Address correspondence to: Karim M. Abadir, Department of Mathematics and Department of Economics, University of York, Heslington, York Y010 5DD, England; e-mail: kma4@york.ac.uk.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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