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 (1988) 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.Résumé. Le but de ce travail porte sur l'estimation d'un modèle autorègressif ayant un bruit exponentiel contaminé. En utilisant la mthode d'approximation d'Andẽl (1988) base sur la stationnarit en moyenne du processus, nous prouvons, moyennant des rsultats analytiques et numriques, que le biais et l'cart quadratique moyen de l'estimateur du maximum de vraisemblance du paramtre sont asymptotiquement stables.
The two sided unit root test of a first-order autoregressive model in the presence of an innovation outlier is considered. In this paper, we present three tests; two are usual and one is new. We give formulas computing the size and the power of the three tests when an innovation outlier (IO) occurs at a specified time, say k. Using a comparative study, we show that the new statistic performs better under contamination. A Small sample case is considered only.
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