Noninvertibility and Pseudo-Maximum Likelihood Estimation of Misspecified ARMA Models

P?tscher, B.M.

Econometric Theory, 1991, vol. 7, issue 04, pages 435-449

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.

Date: 1991

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