Statistical Methods & Applications

, Volume 27, Issue 4, pp 689–714 | Cite as

Testing for an excessive number of zeros in time series of bounded counts

  • Hee-Young Kim
  • Christian H. WeißEmail author
  • Tobias A. Möller
Original Paper


For the modeling of bounded counts, the binomial distribution is a common choice. In applications, however, one often observes an excessive number of zeros and extra-binomial variation, which cannot be explained by a binomial distribution. We propose statistics to evaluate the number of zeros and the dispersion with respect to a binomial model, which is based on the sample binomial index of dispersion and the sample binomial zero index. We apply this index to autocorrelated counts generated by a binomial autoregressive process of order one, which also includes the special case of independent and identically (i. i. d.) bounded counts. The limiting null distributions of the proposed test statistics are derived. A Monte-Carlo study evaluates their size and power under various alternatives. Finally, we present two real-data applications as well as the derivation of effective sample sizes to illustrate the proposed methodology.


Binomial AR(1) model Binomial index of dispersion Binomial zero index Extra-binomial dispersion Extra-binomial zeros Adjusted sample size 

Mathematics Subject Classification

62M10 62F03 



The authors thank the editor and the referees for carefully reading the article and for their comments, which greatly improved the article. Main parts of this research were completed while the first author stayed as a guest professor at the Helmut Schmidt University in Hamburg. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A1B07045707).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Division of Economics and StatisticsKorea UniversitySejongSouth Korea
  2. 2.Department of Mathematics and StatisticsHelmut Schmidt UniversityHamburgGermany

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