# 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

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topBitseki 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 -

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