Convergence results for maximum likelihood type estimators in multivariable ARMA models

Abstract

General convergence results for maximum likelihood type estimators in multivariable ARMA-models under very weak assumptions are given. This extends results by Dunsmuir and Hannan (1976, Advan. Appl. Probab. 8 339-364) and Deistler, Dunsmuir, and Hannan (1978, Advan. Appl. Probab. 10 360-372). In particular it is shown that consistency can be achieved without imposing a certain assumption used in Dunsmuir and Hannan which is related to the zeroes of the spectral density if one is willing to make stronger assumptions concerning the probabilistic structure of the process.ARMA-model likelihood-function consistency misspecification