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Moderate deviations for the Durbin–Watson statistic related tothe first-order autoregressive process
Published online by Cambridge University Press: 03 October 2014
Abstract
The purpose of this paper is to investigate moderate deviations for the Durbin–Watsonstatistic associated with the stable first-order autoregressive process where the drivennoise is also given by a first-order autoregressive process. We first establish a moderatedeviation principle for both the least squares estimator of the unknown parameter of theautoregressive process as well as for the serial correlation estimator associated with thedriven noise. It enables us to provide a moderate deviation principle for theDurbin–Watson statistic in the case where the driven noise is normally distributed and inthe more general case where the driven noise satisfies a less restrictive Chen–Ledoux typecondition.
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- Research Article
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- © EDP Sciences, SMAI 2014
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