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On the Fisher information matrix of a vector ARMA process

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  • Bao, Yong
  • Hua, Ying

Abstract

We derive a neat and compact representation of the asymptotic Fisher information matrix of a vector ARMA process. Its inverse can be used immediately as the asymptotic covariance matrix of the Gaussian maximum likelihood estimator. We also provide the robust sandwich covariance estimator when the process is non-Gaussian.

Suggested Citation

  • Bao, Yong & Hua, Ying, 2014. "On the Fisher information matrix of a vector ARMA process," Economics Letters, Elsevier, vol. 123(1), pages 14-16.
    • Handle: RePEc:eee:ecolet:v:123:y:2014:i:1:p:14-16
    DOI: 10.1016/j.econlet.2014.01.019
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    References listed on IDEAS

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    1. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Thomas J. Sargent & Mark W. Watson, 2007. "ABCs (and Ds) of Understanding VARs," American Economic Review, American Economic Association, vol. 97(3), pages 1021-1026, June.
    2. Klein, André & Mélard, Guy & Saidi, Abdessamad, 2008. "The asymptotic and exact Fisher information matrices of a vector ARMA process," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1430-1433, September.
    3. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    4. André Klein & Guy Melard & Abdessamad Saidi, 2008. "The asymptotic and exact Fisher information matrices," ULB Institutional Repository 2013/13766, ULB -- Universite Libre de Bruxelles.
    5. 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.
    6. Newton, H. Joseph, 1978. "The information matrices of the parameters of multiple mixed time series," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 317-323, June.
    7. 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.
    8. 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.
    9. 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.
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    Cited by:

    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. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    3. 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.
    4. Maddalena Cavicchioli, 2021. "OLS Estimation of Markov switching VAR models: asymptotics and application to energy use," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 431-449, September.
    5. 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.

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    More about this item

    Keywords

    Fisher information matrix; VARMA; Gaussian maximum likelihood estimator;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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