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A note on maximum likelihood estimation in the first-order Gaussian moving average model

Author

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  • Anderson, T. W.
  • Metz, R. P.

Abstract

The likelihoood function of the Gaussian MA(1) zero-mean can be expressed in terms of the variance of the process and the first-order autocorrelation or alternatively in terms of the variance of the unobservable independent normal random variables and the moving average coefficient. The relations between the maximum likelihood estimates of these alternatives pairs are explored. It is noted that in a (finite) sample the maximizing value of the autocorrelation may not correspond to a real value of the moving average coefficient.

Suggested Citation

  • Anderson, T. W. & Metz, R. P., 1993. "A note on maximum likelihood estimation in the first-order Gaussian moving average model," Statistics & Probability Letters, Elsevier, vol. 16(3), pages 205-211, February.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:3:p:205-211
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    Citations

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    Cited by:

    1. Monti, Anna Clara, 1996. "A new preliminary estimator for MA(1) models," Computational Statistics & Data Analysis, Elsevier, vol. 21(1), pages 1-15, January.
    2. van der Leeuw, J.L., 1994. "The second derivative of the likelihood of an exact ARMA model," Other publications TiSEM 04f52885-2820-4b2d-b1f0-b, Tilburg University, School of Economics and Management.
    3. van der Leeuw, J.L., 1994. "The second derivative of the likelihood of an exact ARMA model," Research Memorandum FEW 661, Tilburg University, School of Economics and Management.

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