Poisson QMLE for change-point detection in general integer-valued time series models

Mamadou Lamine Diop () and William Kengne ()
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Mamadou Lamine Diop: CY Cergy Paris Université
William Kengne: CY Cergy Paris Université

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 3, No 5, 373-403

Abstract: Abstract We consider together the retrospective and the sequential change-point detection in a general class of integer-valued time series. The conditional mean of the process depends on a parameter $$\theta ^*$$ θ ∗ which may change over time. We propose procedures which are based on the Poisson quasi-maximum likelihood estimator of the parameter, and where the updated estimator is computed without the historical observations in the sequential framework. For both the retrospective and the sequential detection, the test statistics converge to some distributions obtained from the standard Brownian motion under the null hypothesis of no change and diverge to infinity under the alternative; that is, these procedures are consistent. Some results of simulations as well as real data application are provided.

Keywords: Change-point; Retrospective detection; Sequential detection; Integer-valued time series; Poisson quasi-maximum likelihood; 62M10; 62F05; 62F12; 62L12 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00834-1

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