Noninvertibility and Pseudo-Maximum Likelihood Estimation of Misspecified ARMA Models

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.

Effects of Model Selection on Inference

The asymptotic properties of parameter estimators which are based on a model that has been selected by a model selection procedure are investigated. In particular, the asymptotic distribution is derived and the effects of the model selection process on subsequent inference are illustrated.

On Consistent Statistical Procedures in Regression

Consistency, Orthogonality of measures, Random predictors, Regression,