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Convergence results for maximum likelihood type estimators in multivariable ARMA models


  • Pötscher, B. M.


General convergence results for maximum likelihood type estimators in multivariable ARMA-models under very weak assumptions are given. This extends results by Dunsmuir and Hannan (1976, Advan. Appl. Probab. 8 339-364) and Deistler, Dunsmuir, and Hannan (1978, Advan. Appl. Probab. 10 360-372). In particular it is shown that consistency can be achieved without imposing a certain assumption used in Dunsmuir and Hannan which is related to the zeroes of the spectral density if one is willing to make stronger assumptions concerning the probabilistic structure of the process.

Suggested Citation

  • Pötscher, B. M., 1987. "Convergence results for maximum likelihood type estimators in multivariable ARMA models," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 29-52, February.
  • Handle: RePEc:eee:jmvana:v:21:y:1987:i:1:p:29-52

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    Cited by:

    1. Findley, David F. & Potscher, Benedikt M. & Wei, Ching-Zong, 2004. "Modeling of time series arrays by multistep prediction or likelihood methods," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 151-187.
    2. Bühlmann, Peter, 1995. "Moving-average representation of autoregressive approximations," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 331-342, December.


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