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Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models

S. Valère Bitseki Penda;  Hacène Djellout — 2014

Annales de l'I.H.P. Probabilités et statistiques

The purpose of this paper is to investigate the deviation inequalities and the moderate deviation principle of the least squares estimators of the unknown parameters of general p th-order asymmetric bifurcating autoregressive processes, under suitable assumptions on the driven noise of the process. Our investigation relies on the moderate deviation principle for martingales.

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

S. Valère Bitseki Penda;  Hacène Djellout;  Frédéric Proïa — 2014

ESAIM: Probability and Statistics

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...

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