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Noninvertibility and Pseudo-Maximum Likelihood Estimation of Misspecified ARMA Models

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  • Pötscher, B.M.

Abstract

Recently Tanaka and Satchell [11] investigated the limiting properties of local maximizers of the Gaussian pseudo-likelihood function of a misspecified moving average model of order one in case the spectral density of the data process has a zero at frequency zero. We show that pseudo-maximum likelihood estimators in the narrower sense, that is, global maximizers of the Gaussian pseudo-likelihood function, may exhibit behavior drastically different from that of the local maximizers. Some general results on the limiting behavior of pseudo-maximum likelihood estimators in potentially misspecified ARMA models are also presented.

Suggested Citation

  • Pötscher, B.M., 1991. "Noninvertibility and Pseudo-Maximum Likelihood Estimation of Misspecified ARMA Models," Econometric Theory, Cambridge University Press, vol. 7(04), pages 435-449, December.
  • Handle: RePEc:cup:etheor:v:7:y:1991:i:04:p:435-449_00
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    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. Luukkonen, Ritva & Saikkonen, Pentti, 1996. "Power of the Lagrange multiplier test for testing an autoregressive unit root," Economics Letters, Elsevier, vol. 51(1), pages 27-35, April.
    3. Vougas, Dimitrios V., 2008. "New exact ML estimation and inference for a Gaussian MA(1) process," Economics Letters, Elsevier, vol. 99(1), pages 172-176, April.
    4. Guyon, Xavier & Yao, Jian-feng, 1999. "On the Underfitting and Overfitting Sets of Models Chosen by Order Selection Criteria," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 221-249, August.

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