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Computation of the Fisher information matrix for SISO models

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  • André Klein
  • Guy Melard

Abstract

Closed form expressions and an algorithm for obtaining the Fisher information matrix of Gaussian single input single output (SISO) time series models are presented. It enables the computation of the asymptotic covariance matrix of maximum likelihood estimators of the parameters. The procedure makes use of the autocovariance function of one or more autoregressive processes. Under certain conditions, the SISO model can be a special case of a vector autoregressive moving average (ARMA) model, for which there is a method to evaluate the Fisher information matrix. That method is compared with the procedure described in the paper. © 1994 IEEE

Suggested Citation

  • André Klein & Guy Melard, 1994. "Computation of the Fisher information matrix for SISO models," ULB Institutional Repository 2013/13728, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/13728
    Note: SCOPUS: ar.j
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    1. André Klein & Guy Melard, 1990. "Fisher's information matrix for seasonal autoregressive-moving average models," ULB Institutional Repository 2013/13718, ULB -- Universite Libre de Bruxelles.
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    Cited by:

    1. André Klein & Guy Melard & Toufik Zahaf, 1998. "Computation of the exact information matrix of Gaussian dynamic regression time series models," ULB Institutional Repository 2013/13738, ULB -- Universite Libre de Bruxelles.
    2. Abdelhamid Ouakasse & Guy Mélard, 2017. "A New Recursive Estimation Method for Single Input Single Output Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(3), pages 417-457, May.
    3. André Klein & Guy Mélard, 2004. "An algorithm for computing the asymptotic fisher information matrix for seasonal SISO models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 627-648, September.
    4. Abdelhamid Ouakasse & Guy Melard, 2002. "Estimation en ligne pour le modèle ARMA," ULB Institutional Repository 2013/13826, ULB -- Universite Libre de Bruxelles.
    5. André Klein & Guy Melard, 1995. "Computation of the Fisher information matrix for time series models," ULB Institutional Repository 2013/13736, ULB -- Universite Libre de Bruxelles.
    6. André Klein & Guy Melard, 2004. "An algorithm for computing the asymptotic Fisher information matrix for seasonal SISO models," ULB Institutional Repository 2013/13746, ULB -- Universite Libre de Bruxelles.
    7. André Klein & Guy Melard & Abdessamad Saidi, 2008. "The asymptotic and exact Fisher information matrices," ULB Institutional Repository 2013/13766, ULB -- Universite Libre de Bruxelles.

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    1. André Klein & Guy Melard & Toufik Zahaf, 1998. "Computation of the exact information matrix of Gaussian dynamic regression time series models," ULB Institutional Repository 2013/13738, ULB -- Universite Libre de Bruxelles.
    2. André Klein & Guy Melard, 1994. "The information matrix of multiple input single output time series models," ULB Institutional Repository 2013/13732, ULB -- Universite Libre de Bruxelles.
    3. André Klein & Guy Melard, 1995. "Computation of the Fisher information matrix for time series models," ULB Institutional Repository 2013/13736, ULB -- Universite Libre de Bruxelles.
    4. Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012. "Computing and estimating information matrices of weak ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 345-361.
    5. André Klein & Guy Mélard, 2004. "An algorithm for computing the asymptotic fisher information matrix for seasonal SISO models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 627-648, September.
    6. Klein, A. & Spreij, P., 1993. "On Fisher's information matrix of an ARMA process and Sylvester's resultant matrix," Serie Research Memoranda 0033, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    7. André Klein & Guy Melard, 2004. "An algorithm for computing the asymptotic Fisher information matrix for seasonal SISO models," ULB Institutional Repository 2013/13746, ULB -- Universite Libre de Bruxelles.

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