BITSEKI PENDA, Valère; DJELLOUT, Hacène; PROÏA, Frédéric

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BITSEKI PENDA, Valère
Laboratoire de Mathématiques Blaise Pascal [LMBP]

DJELLOUT, Hacène
Laboratoire de Mathématiques Blaise Pascal [LMBP]

PROÏA, Frédéric
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]

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Document de travail - Pré-publication

Resumen en inglés

The purpose of this paper is to investigate moderate deviations for the Durbin-Watson statistic associated with the stable first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We first establish a moderate deviation principle for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise. It enables us to provide a moderate deviation principle for the Durbin-Watson statistic in the easy case where the driven noise is normally distributed and in the more general case where the driven noise satisfies a less restrictive Chen-Ledoux type condition.< Leer menos

Palabras clave en inglés

Durbin-Watson statistic

Moderate deviation principle

First-order autoregressive process

Serial correlation

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Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251