Noninvertibility and Pseudo-Maximum Likelihood Estimation of Misspecified ARMA Models
研究了误设定ARMA模型中，全局伪极大似然估计量的极限行为与局部极大值点截然不同，并给出了更一般的结果。
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.