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


H Fella
L Atil
C Belkacem

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 Andel (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.

Le but de ce travail porte sur l'estimation d'un modele autoregressif ayant un bruit exponentiel contamine. En utilisant la mthode d'approximation d'Andel (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.


Key words: Autoregressive; Contamination; Exponential; Estimation; Stability.


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print ISSN: 2316-090X