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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(4), 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. James Morley & Irina B. Panovska & Tara M. Sinclair, 2013. "Testing Stationarity for Unobserved Components Models," Discussion Papers 2012-41A, School of Economics, The University of New South Wales.
    5. Potscher, Benedikt M., 1995. "Comment on 'Adaptive estimation in time series regression models' by D.G. Steigerwald," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 123-129.
    6. 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.
    7. James Morley & Irina B. Panovska & Tara M. Sinclair, 2014. "Testing Stationarity for Unobserved Components Models," Discussion Papers 2012-41B, School of Economics, The University of New South Wales.

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