On the stability of estimation of AR(1) coefficient in the presence of contaminated exponential innovations

Abstract

The aim of our paper is to present an exhaustive study of the estimation of first order autoregressive models with exponential white noise under innovation contamination. Some theoretical aspects and Monte Carlo results are presented in the study of the stability of this estimator when the model is contaminated. Using the methodology of Andẽl based on the mean stationarity of the process, we prove that the maximum likelihood estimator of the parameter is asymptotically stable with respect to the bias and the mean square error. Also, some results of the small sample case are obtained.

Le but de ce travail porte sur l'estimation d'un modèle autorègressif ayant un bruit exponentiel contaminé. En utilisant la méthode d'approximation d'Andẽl basée sur la stationnarité en moyenne du processus, nous prouvons, moyennant des résultats analytiques et numériques, que le biais et l'écart quadratique moyen de l'estimateur du maximum de vraisemblance du paramètre sont asymptotiquement stables.