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On the Evaluation of the Information Matrix for Multiplicative Seasonal Time‐Series Models

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  • E. J. Godolphin
  • S. R. Bane

Abstract

. This paper gives a procedure for evaluating the Fisher information matrix for a general multiplicative seasonal autoregressive moving average time‐series model. The method is based on the well‐known integral specification of Whittle [Ark. Mat. Fys. Astr. (1953) vol. 2. pp. 423–434] and leads to a system of linear equations, which is independent of the seasonal period and has a closed solution. It is shown to be much simpler, in general, than the method of Klein and Mélard [Journal of Time Series Analysis (1990) vol. 11, pp. 231–237], which depends on the seasonal period. It is also shown that the nonseasonal method of McLeod [Biometrika (1984) vol. 71, pp. 207–211] has the same basic features as that of Klein and Mélard. Explicit solutions are obtained for the simpler nonseasonal and seasonal models in common use, a feature which has not been attempted with the Klein–Mélard or the McLeod approaches. Several illustrations of these results are discussed in detail.

Suggested Citation

  • E. J. Godolphin & S. R. Bane, 2006. "On the Evaluation of the Information Matrix for Multiplicative Seasonal Time‐Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 167-190, March.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:2:p:167-190
    DOI: 10.1111/j.1467-9892.2005.00461.x
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    Cited by:

    1. 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.
    2. Bao, Yong & Hua, Ying, 2014. "On the Fisher information matrix of a vector ARMA process," Economics Letters, Elsevier, vol. 123(1), pages 14-16.

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