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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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  • Forchini, G.

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

  • Forchini, G., 2000. "The density of the sufficient statistics for a Gaussian AR(1) model in terms of generalized functions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 237-243, November.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:3:p:237-243
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    References listed on IDEAS

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    1. 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.
    2. Chikuse, Yasuko, 1987. "Methods for Constructing Top Order Invariant Polynomials," Econometric Theory, Cambridge University Press, vol. 3(2), pages 195-207, April.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
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    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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