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An algorithm for computing the asymptotic Fisher information matrix for seasonal SISO models

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  • André Klein
  • Guy Melard

Abstract

The paper presents an algorithm for computing the asymptotic Fisher information matrix of a possibly seasonal single-input single-output (SISO) time-series model. That matrix is a block matrix whose elements are basically integrals of rational functions over the oriented unit circle. The procedure makes use of the autocovariance or the cross-covariance function of two autoregressive processes based on the same noise. The algorithm also works when the input variable is omitted, the case of a seasonal ARMA model.

Suggested Citation

  • 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.
    • Handle: RePEc:ulb:ulbeco:2013/13746
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    References listed on IDEAS

    as
    1. Mittnik, Stefan & Zadrozny, Peter A, 1993. "Asymptotic Distributions of Impulse Responses, Step Responses, and Variance Decompositions of Estimated Linear Dynamic Models," Econometrica, Econometric Society, vol. 61(4), pages 857-870, July.
    2. André Klein & Guy Melard, 1989. "On algorithms for computing the covariance matrix of estimates in autoregresive-moving average processes," ULB Institutional Repository 2013/13710, ULB -- Universite Libre de Bruxelles.
    3. André Klein & Guy Melard, 1994. "Computation of the Fisher information matrix for SISO models," ULB Institutional Repository 2013/13728, ULB -- Universite Libre de Bruxelles.
    4. 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.
    5. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
    6. André Klein & Guy Melard & Toufik Zahaf, 2000. "Construction of the exact Fisher information matrix of Gaussian time series models by means of matrix differential rules," ULB Institutional Repository 2013/13742, ULB -- Universite Libre de Bruxelles.
    7. Marc Hallin & Bas Werker, 1998. "Optimal testing for semiparametric autoregressive models: from Gaussian Lagrange multipliers to regression rank scores and adaptive tests," ULB Institutional Repository 2013/2219, ULB -- Universite Libre de Bruxelles.
    8. 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.
    9. Peter A. Zadrozny, 1988. "Analytic Derivatives for Estimation of Linear Dynamic Models," Working Papers 88-5, Center for Economic Studies, U.S. Census Bureau.
    10. 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. 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.
    2. 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.

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