hal-00661075, version 1

Moderate deviations for the Durbin-Watson statistic related to the first-order autoregressive process

Valère Bitseki Penda () ¹, Hacène Djellout () ¹, Frédéric Proïa (, ) ^2, 3

(2012-01-17)

• 1:  Laboratoire de Mathématiques
• http://math.univ-bpclermont.fr/index.html
  CNRS : UMR6620 – Université Blaise Pascal - Clermont-Ferrand II 24 avenue des Landais 63177 AUBIERE CEDEX France
• 2:  Institut de Mathématiques de Bordeaux (IMB)
• http://www.math.u-bordeaux.fr/IMB/
  CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II 351 cours de la Libération 33405 TALENCE CEDEX France
• 3:  ALEA (INRIA Bordeaux - Sud-Ouest)
• 
  INRIA – Université de Bordeaux – CNRS : UMR5251 France

Bibliographic reference

• Type of document: Documents without publication reference (Preprint)
• Subject:

  Mathematics/Statistics

  Statistics/Statistics Theory

  Mathematics/Probability

• Title: Moderate deviations for the Durbin-Watson statistic related to the first-order autoregressive process
• Abstract: 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.
• Fulltext language: English
• Production date: 2012-01-17
• Keyword(s): Durbin-Watson statistic – Moderate deviation principle – First-order autoregressive process – Serial correlation
• Classification: 60F10 ; 60G42 ; 62M10 ; 62G05
• Comment: 24 pages.

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• hal-00661075, version 1
• http://hal.archives-ouvertes.fr/hal-00661075
• oai:hal.archives-ouvertes.fr:hal-00661075
• From: Frédéric Proia <>
• Submitted on: Wednesday, 18 January 2012 14:35:15
• Updated on: Wednesday, 18 January 2012 16:48:06