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 \(\theta ^*\) 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.
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The authors are grateful to the Editor, the Associate Editor and the two anonymous Referees for many relevant suggestions and comments which helped to improve the contents of this article.
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M. L. Diop and W. Kengne: Supported by the MME-DII center of excellence (ANR-11-LABEX-0023-01) and the ANR BREAKRISK: ANR-17-CE26-0001-01. W. Kengne: Developed within the CY Initiative of Excellence (Grant “Investissements d’Avenir” ANR-16-IDEX-0008), Project “EcoDep” PSI-AAP2020-0000000013.
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Diop, M.L., Kengne, W. Poisson QMLE for change-point detection in general integer-valued time series models. Metrika 85, 373–403 (2022). https://doi.org/10.1007/s00184-021-00834-1
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DOI: https://doi.org/10.1007/s00184-021-00834-1
Keywords
- Change-point
- Retrospective detection
- Sequential detection
- Integer-valued time series
- Poisson quasi-maximum likelihood