Testing for zero inflation and overdispersion in INAR(1) models
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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.
KeywordsDiscrete data models Overdispersion Zero-inflation Count data time series Dispersion index Zero indexes
Mathematics Subject Classification60J10 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.
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