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

Karim Abadir () and Rolf Larsson

Econometric Theory, 2001, vol. 17, issue 01, pages 222-246

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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