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The Poisson INAR(1) CUSUM chart under overdispersion and estimation error

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  • Christian Weiß
  • Murat Testik

Abstract

The Poisson INAR(1) CUSUM chart has been proposed to monitor integer-valued autoregressive processes of order 1 with Poisson marginals. The effectiveness of this chart has been shown under the assumptions of Poisson marginals and known in-control process parameters, but these assumptions may not be very well satisfied in practical applications. This article investigates the practical issues concerning applications of the Poisson INAR(1) CUSUM chart, considering average run lengths obtained through a bivariate Markov chain approach. First, the effects of deviations from the assumed Poisson model are investigated when there is overdispersion. Design recommendations for achieving robustness are provided along with an extension, the Winsorized Poisson INAR(1) CUSUM chart. Next, analyzing the conditional average run length performance under some hypothetical cases of parameter estimation, it is shown that estimation errors may severely affect the chart’s performance. The marginal average run length performance is used to derive sample size recommendations. An example for monitoring the number of beds occupied at a hospital emergency department is used to illustrate the proposed approach.

Suggested Citation

  • Christian Weiß & Murat Testik, 2011. "The Poisson INAR(1) CUSUM chart under overdispersion and estimation error," IISE Transactions, Taylor & Francis Journals, vol. 43(11), pages 805-818.
    • Handle: RePEc:taf:uiiexx:v:43:y:2011:i:11:p:805-818
    DOI: 10.1080/0740817X.2010.550910
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    Cited by:

    1. Sofia Paulino & Manuel Cabral Morais & Sven Knoth, 2019. "On ARL-unbiased c-charts for INAR(1) Poisson counts," Statistical Papers, Springer, vol. 60(4), pages 1021-1038, August.
    2. Yunwei Cui & Rongning Wu & Qi Zheng, 2021. "Estimation of change‐point for a class of count time series models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1277-1313, December.
    3. Youngmi Lee & Sangyeol Lee, 2019. "CUSUM test for general nonlinear integer-valued GARCH models: comparison study," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1033-1057, October.
    4. Mamadou Lamine Diop & William Kengne, 2022. "Poisson QMLE for change-point detection in general integer-valued time series models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 373-403, April.

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