On ar(1) processes with exponential white noise

Anděl, Jiří

doi:10.1080/03610928808829693

Cited by 41 publications

(20 citation statements)

References 3 publications

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“…We proved that the methodology of Andẽl (1988) is valid under this contaminated model. Finally, we showed that the MLE is asymtotically robust with respect to the bias and MSE and is stable if the contaminant α varies between a suitable value α s computed numerically and one, even in small sample case.…”

Section: Discussionmentioning

confidence: 83%

“…Since the process is stationary with mean m = 1/(1 − ρ), he proposed to substitute m for X t−1 in (3). Then the estimator becomes Andẽl (1988) found then the distribution for this new modified estimator of ρ. Consistency results for higher-order processes are given by Andẽl (1988) and An and Huang (1993).…”

Section: The Modelmentioning

confidence: 99%

“…Moreover, Andẽl (1988) considered the following modification. Since the process is stationary with mean m = 1/(1 − ρ), he proposed to substitute m for X t−1 in (3).…”

Section: The Modelmentioning

confidence: 99%

“…Now, assume that 0 ≤ ρ ≤ 1 and all what we observe is a segment of the process X 1 , X 2 , ..., X n , n fixed (2) with ρ unknown and is to be estimated. Andẽl (1988), in order to obtain the mean stationarity of the process, we assume that X 0 is distributed according to Exp(1 − ρ). The maximum likelihood estimator for ρ is…”

Section: The Modelmentioning

confidence: 99%

“…In Andẽl and Zvãra (1988), tables of the bias and variance of ρ are given using numerical approximations. Moreover, Andẽl (1988) considered the following modification.…”

Section: The Modelmentioning

confidence: 99%

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

Fellag¹,

Atil²,

Belkacem³

2014

jas

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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.

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Section: Discussionmentioning

confidence: 83%

Section: The Modelmentioning

confidence: 99%

“…Moreover, Andẽl (1988) considered the following modification. Since the process is stationary with mean m = 1/(1 − ρ), he proposed to substitute m for X t−1 in (3).…”

Section: The Modelmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

“…In Andẽl and Zvãra (1988), tables of the bias and variance of ρ are given using numerical approximations. Moreover, Andẽl (1988) considered the following modification.…”

Section: The Modelmentioning

confidence: 99%

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