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

S. Valère Bitseki Penda; Hacène Djellout; Frédéric Proïa

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 308-331
  • ISSN: 1292-8100

Abstract

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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 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.

How to cite

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Bitseki Penda, S. Valère, Djellout, Hacène, and Proïa, Frédéric. "Moderate deviations for the Durbin–Watson statistic related to the first-order autoregressive process." ESAIM: Probability and Statistics 18 (2014): 308-331. <http://eudml.org/doc/274345>.

@article{BitsekiPenda2014,
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 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.},
author = {Bitseki Penda, S. Valère, Djellout, Hacène, Proïa, Frédéric},
journal = {ESAIM: Probability and Statistics},
keywords = {Durbin–Watson statistic; moderate deviation principle; first-order autoregressive process; serial correlation; Durbin-Watson statistic; moderate deviations principle},
language = {eng},
pages = {308-331},
publisher = {EDP-Sciences},
title = {Moderate deviations for the Durbin–Watson statistic related to the first-order autoregressive process},
url = {http://eudml.org/doc/274345},
volume = {18},
year = {2014},
}

TY - JOUR
AU - Bitseki Penda, S. Valère
AU - Djellout, Hacène
AU - Proïa, Frédéric
TI - Moderate deviations for the Durbin–Watson statistic related to the first-order autoregressive process
JO - ESAIM: Probability and Statistics
PY - 2014
PB - EDP-Sciences
VL - 18
SP - 308
EP - 331
AB - 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 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.
LA - eng
KW - Durbin–Watson statistic; moderate deviation principle; first-order autoregressive process; serial correlation; Durbin-Watson statistic; moderate deviations principle
UR - http://eudml.org/doc/274345
ER -

References

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