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Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models

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  • José Alberto Mauricio Arias

    (Departamento de Análisis Económico y Economía Cuantitativa. Facultad de Ciencias Económicas y Empresariales. Universidad Complutense Madrid.)

Abstract

The problems of evaluating and maximizing the exact likelihood function of vector ARMA models are considered separately. A new and efficient procedure for evaluating the exact likelihood function is presented. This method puts together a set of useful features which can only be found separately in currently available algorithms. A procedure for maximizing the exact likelihood function, which takes full advantage of the properties offered by the evaluation algorithm, is also considered. Combining these two procedures, a new algorithm for exact maximum likelihood estimation of vector ARMA models is obtained. Comparisons with existing procedures, in terms of both analytical arguments and a numerical example, are given in order to show that the new estimation algorithm performs at least as well as existing ones, and that relevant real situations occur in which it do es better.

Suggested Citation

  • José Alberto Mauricio Arias, 1993. "Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models," Documentos de Trabajo del ICAE 9316, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:9316
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    File URL: https://eprints.ucm.es/id/eprint/28778/1/9316.pdf
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    References listed on IDEAS

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    1. Sergio Koreisha & Tarmo Pukkila, 1989. "Fast Linear Estimation Methods For Vector Autoregressive Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(4), pages 325-339, July.
    2. Ansley, Craig F. & Newbold, Paul, 1980. "Finite sample properties of estimators for autoregressive moving average models," Journal of Econometrics, Elsevier, vol. 13(2), pages 159-183, June.
    3. B. L. Shea, 1987. "Estimation Of Multivariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 95-109, January.
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    1. José Alberto Mauricio Arias, 1993. "The exact likelihood function for the vector ARMA model," Documentos de Trabajo del ICAE 9317, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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