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Goodness‐of‐fit tests for Poisson count time series based on the Stein–Chen identity

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  • Boris Aleksandrov
  • Christian H. Weiß
  • Carsten Jentsch

Abstract

To test the null hypothesis of a Poisson marginal distribution, test statistics based on the Stein–Chen identity are proposed. For a wide class of Poisson count time series, the asymptotic distribution of different types of Stein–Chen statistics is derived, also if multiple statistics are jointly applied. The performance of the tests is analyzed with simulations, as well as the question which Stein–Chen functions should be used for which alternative. Illustrative data examples are presented, and possible extensions of the novel Stein–Chen approach are discussed as well.

Suggested Citation

  • Boris Aleksandrov & Christian H. Weiß & Carsten Jentsch, 2022. "Goodness‐of‐fit tests for Poisson count time series based on the Stein–Chen identity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 35-64, February.
    • Handle: RePEc:bla:stanee:v:76:y:2022:i:1:p:35-64
    DOI: 10.1111/stan.12252
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    References listed on IDEAS

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    1. Boris Aleksandrov & Christian H. Weiß, 2020. "Testing the dispersion structure of count time series using Pearson residuals," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 325-361, September.
    2. Boris Aleksandrov & Christian H. Weiß, 2020. "Parameter estimation and diagnostic tests for INMA(1) processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 196-232, March.
    3. Zhu, Fukang & Wang, Dehui, 2010. "Diagnostic checking integer-valued ARCH(p) models using conditional residual autocorrelations," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 496-508, February.
    4. Doukhan, Paul & Fokianos, Konstantinos & Li, Xiaoyin, 2012. "On weak dependence conditions: The case of discrete valued processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1941-1948.
    5. Sebastian Schweer & Christian H. Weiß, 2016. "Testing for Poisson arrivals in INAR(1) processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 503-524, September.
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