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A note on the asymptotic and exact Fisher information matrices of a Markov switching VARMA process

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  • Maddalena Cavicchioli

    (University of Modena and Reggio Emilia)

Abstract

We study the asymptotic and exact Fisher information (FI) matrices of Markov switching vector autoregressive moving average (MS VARMA) models. In a related paper (2017), we propose a method to derive an explicit expression in closed form for the asymptotic FI matrix of the underlying model, and use such a matrix to derive the asymptotic covariance matrix of the Gaussian maximum likelihood (ML) estimator of the parameters in the MS VARMA model. In this paper, the exact FI matrix of a Gaussian MS VARMA process is considered for a time series of length T in relation to the exact ML estimation method. Furthermore, we prove that the Gaussian exact FI matrix converges in probability to the asymptotic FI matrix when the sample size T goes to infinity.

Suggested Citation

  • Maddalena Cavicchioli, 2020. "A note on the asymptotic and exact Fisher information matrices of a Markov switching VARMA process," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 129-139, March.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:1:d:10.1007_s10260-019-00472-y
    DOI: 10.1007/s10260-019-00472-y
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    References listed on IDEAS

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    1. Cavicchioli, Maddalena, 2017. "Asymptotic Fisher information matrix of Markov switching VARMA models," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 124-135.
    2. André Klein & Guy Melard & Abdessamad Saidi, 2008. "The asymptotic and exact Fisher information matrices," ULB Institutional Repository 2013/13766, ULB -- Universite Libre de Bruxelles.
    3. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    4. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    5. Bao, Yong & Hua, Ying, 2014. "On the Fisher information matrix of a vector ARMA process," Economics Letters, Elsevier, vol. 123(1), pages 14-16.
    6. Maddalena Cavicchioli, 2014. "Analysis Of The Likelihood Function For Markov-Switching Var(Ch) Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 624-639, November.
    7. Yang, Minxian, 2000. "Some Properties Of Vector Autoregressive Processes With Markov-Switching Coefficients," Econometric Theory, Cambridge University Press, vol. 16(1), pages 23-43, February.
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