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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 {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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  • Abadir, Karim M. & Larsson, Rolf, 2001. "The Joint Moment Generating Function Of Quadratic Forms In Multivariate Autoregressive Series," Econometric Theory, Cambridge University Press, vol. 17(1), pages 222-246, February.
    • Handle: RePEc:cup:etheor:v:17:y:2001:i:01:p:222-246_17
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    Cited by:

    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.
    2. Marcus J. Chambers, 2015. "The Calculation of Some Limiting Distributions Arising in Near-Integrated Models with GLS Detrending," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 562-586, July.
    3. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.

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