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The Density of the Sufficient Statistics for a Gaussian AR(1) Model in Terms of Generalized Functions

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  • Giovanni Forchini

Abstract

This paper derives the exact joint distribution of the minimal sufficient statistics in the first-order AR(1) model with Gaussian errors and zero start-up value. The results are fundamental to an exact distribution theory for the statistics that are typically of interest in this model.

Suggested Citation

  • Giovanni Forchini, "undated". "The Density of the Sufficient Statistics for a Gaussian AR(1) Model in Terms of Generalized Functions," Discussion Papers 00/06, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:00/06
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    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2000/0006.pdf
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    References listed on IDEAS

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    1. Chikuse, Yasuko, 1987. "Methods for Constructing Top Order Invariant Polynomials," Econometric Theory, Cambridge University Press, vol. 3(2), pages 195-207, April.
    2. Chikuse, Yasuko & Davis, A. W., 1986. "A Survey on the Invariant Polynomials with Matrix Arguments in Relation to Econometric Distribution Theory," Econometric Theory, Cambridge University Press, vol. 2(2), pages 232-248, August.
    3. Vinod, H.D. & Shenton, L.R., 1996. "Exact Moments for Autor1egressive and Random walk Models for a Zero or Stationary Initial Value," Econometric Theory, Cambridge University Press, vol. 12(3), pages 481-499, August.
    4. van GARDEREN, Kees Jan, 1997. "Exact geometry of explosive autoregressive models," LIDAM Discussion Papers CORE 1997068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
    6. Nankervis, J. C. & Savin, N. E., 1988. "The exact moments of the least-squares estimator for the autoregressive model corrections and extensions," Journal of Econometrics, Elsevier, vol. 37(3), pages 381-388, March.
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    Cited by:

    1. Amo-Salas, M. & López-Fidalgo, J. & Pedregal, D.J., 2015. "Experimental designs for autoregressive models applied to industrial maintenance," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 87-94.

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    Keywords

    Gaussian AR(1); Generalized Functions.;

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