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Testing for zero inflation and overdispersion in INAR(1) models

Author

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  • Christian H. Weiß

    (Helmut Schmidt University)

  • Annika Homburg

    (Helmut Schmidt University)

  • Pedro Puig

    (Universitat Autònoma de Barcelona)

Abstract

The marginal distribution of count data processes rarely follows a simple Poisson model in practice. Instead, one commonly observes deviations such as overdispersion or zero inflation. To express the extend of such deviations from a Poisson model, one can compute an appropriately defined dispersion index or zero index. In this article, we develop several tests based on such indexes, including joint tests being based on an index combination. The asymptotic distribution of the resulting test statistics under the null hypothesis of a Poisson INAR(1) model is derived, and the finite-sample performance of the resulting tests is analyzed. Real data examples illustrate the application of these tests in practice.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:3:d:10.1007_s00362-016-0851-y
    DOI: 10.1007/s00362-016-0851-y
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    References listed on IDEAS

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    1. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
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    4. Simos Meintanis & Dimitris Karlis, 2014. "Validation tests for the innovation distribution in INAR time series models," Computational Statistics, Springer, vol. 29(5), pages 1221-1241, October.
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    8. Mònica Pujol & Joan-Francesc Barquinero & Pedro Puig & Roser Puig & María Rosa Caballín & Leonardo Barrios, 2014. "A New Model of Biodosimetry to Integrate Low and High Doses," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-19, December.
    9. Wagner Barreto-Souza, 2015. "Zero-Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 839-852, November.
    10. 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.
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    Cited by:

    1. Boris Aleksandrov & Christian H. Weiß & Simon Nik & Maxime Faymonville & Carsten Jentsch, 2024. "Modelling and diagnostic tests for Poisson and negative-binomial count time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(7), pages 843-887, October.

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