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Detecting overdispersion in INARCH(1) processes

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  • Christian H. Weiß
  • Sebastian Schweer

Abstract

type="main" xml:id="stan12059-abs-0001"> A statistical test for the degree of overdispersion of count data time series based on the empirical version of the (Poisson) index of dispersion is considered. The test design relies on asymptotic properties of this index of dispersion, which in turn have been analyzed for time series stemming from a compound Poisson (Poisson-stopped sum) INAR(1) model. This approach is extended to the popular Poisson INARCH(1) model, which exhibits unconditional overdispersion but has an (equidispersed) conditional Poisson distribution. The asymptotic distribution of the index of dispersion if applied to time series stemming from such a model is derived. These results allow us to investigate the ability of the dispersion test to discriminate between Poisson INAR(1) and INARCH(1) models. Furthermore, the question is considered if the index of dispersion could be used to test the null of a Poisson INARCH(1) model against the alternative of an INARCH(1) model with additional conditional overdispersion.

Suggested Citation

  • Christian H. Weiß & Sebastian Schweer, 2015. "Detecting overdispersion in INARCH(1) processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 281-297, August.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:3:p:281-297
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    References listed on IDEAS

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    7. Xu, Hai-Yan & Xie, Min & Goh, Thong Ngee & Fu, Xiuju, 2012. "A model for integer-valued time series with conditional overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4229-4242.
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    Cited by:

    1. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2021. "Goodness–of–Fit Tests for Bivariate Time Series of Counts," Econometrics, MDPI, vol. 9(1), pages 1-20, March.
    2. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2024. "Specifications tests for count time series models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(4), pages 1014-1040, December.
    3. Weiß, Christian H. & Schweer, Sebastian, 2016. "Bias corrections for moment estimators in Poisson INAR(1) and INARCH(1) processes," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 124-130.
    4. 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.
    5. Christian H. Weiß & Annika Homburg & Pedro Puig, 2019. "Testing for zero inflation and overdispersion in INAR(1) models," Statistical Papers, Springer, vol. 60(3), pages 823-848, June.

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