Moderate deviations for the Durbinâ€"Watson statistic related to the first-order autoregressive process. (3rd October 2014)

• Record Type: Journal Article
• Authors: Bitseki Penda, S. Valère; Djellout, Hacène; Proïa, Frédéric
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 308
• Page End: 331
• Publication Date: 2014-10-03
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2013038
• Languages: English
• ISSNs: 1292-8100

Abstract

<abstract abstract-type="normal" xml:lang="en"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>The purpose of this paper is to investigate moderate deviations for the Durbinâ€"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 Durbinâ€"Watson statistic in the case where the driven noise is normally distributed and in the more general case where the driven noise satisfies a less restrictive Chenâ€"Ledoux type condition.</p> </abstract>