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

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  • Abadir, Karim M.
  • Larsson, Rolf

Abstract

Let (X1) be a discrete multivariate Gaussian autoregressive process of order 1. The paper derives the exact finite-sample joint moment generating function (m.g.f.) of the three quadratic forms constituting the sufficient statistic of the process. The formula is then specialized to some cases of interest, including the m.g.f. of functional of multivariate Ornstein-Uhlenbeck processes that arise asymptotically from more general (X1) processes as well.

Suggested Citation

  • Abadir, Karim M. & Larsson, Rolf, 1996. "The Joint Moment Generating Function of Quadratic Forms in Multivariate Autoregressive Series," Econometric Theory, Cambridge University Press, vol. 12(4), pages 682-704, October.
    • Handle: RePEc:cup:etheor:v:12:y:1996:i:04:p:682-704_00
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    1. Lawford, Steve & Stamatogiannis, Michalis P., 2009. "The finite-sample effects of VAR dimensions on OLS bias, OLS variance, and minimum MSE estimators," Journal of Econometrics, Elsevier, vol. 148(2), pages 124-130, February.

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