Statistical Papers

, Volume 60, Issue 3, pp 823–848 | Cite as

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

  • Christian H. WeißEmail author
  • Annika Homburg
  • Pedro Puig
Regular Article


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.


Discrete data models Overdispersion Zero-inflation Count data time series Dispersion index Zero indexes 

Mathematics Subject Classification

60J10 62M02 62F12 



The authors are grateful to two referees for useful comments on an earlier draft of this article. The authors would also like to thank Tobias Möller, Helmut Schmidt University Hamburg, for making them aware of the Regensburg time series studied in Sect. 5.2. The third author was funded by the Grants MTM2012-31118 and MTM2015-69493-R from the Spanish Ministry of Economy and Competitiveness.

Supplementary material

362_2016_851_MOESM1_ESM.pdf (211 kb)
Supplementary material 1 (pdf 210 KB)
362_2016_851_MOESM2_ESM.pdf (1.1 mb)
Supplementary material 2 (pdf 1119 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsHelmut Schmidt UniversityHamburgGermany
  2. 2.Department of MathematicsUniversitat Autònoma de BarcelonaBarcelonaSpain

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