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

Author

Listed:
  • Hee-Young Kim

    (Korea University)

  • Christian H. Weiß

    (Helmut Schmidt University)

  • Tobias A. Möller

    (Helmut Schmidt University)

Abstract

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.

Suggested Citation

  • Hee-Young Kim & Christian H. Weiß & Tobias A. Möller, 2018. "Testing for an excessive number of zeros in time series of bounded counts," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 689-714, December.
    • Handle: RePEc:spr:stmapp:v:27:y:2018:i:4:d:10.1007_s10260-018-00431-z
    DOI: 10.1007/s10260-018-00431-z
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    References listed on IDEAS

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    1. Tobias A. Möller & Christian H. Weiß & Hee-Young Kim & Andrei Sirchenko, 2018. "Modeling Zero Inflation in Count Data Time Series with Bounded Support," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 589-609, June.
    2. D. Böhning & E. Dietz & P. Schlattmann & L. Mendonça & U. Kirchner, 1999. "The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 195-209.
    3. Puig, Pedro & Valero, Jordi, 2006. "Count Data Distributions: Some Characterizations With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 332-340, March.
    4. Christian H. Weiß & Philip K. Pollett, 2012. "Chain Binomial Models and Binomial Autoregressive Processes," Biometrics, The International Biometric Society, vol. 68(3), pages 815-824, September.
    5. Gurutzeta Guillera-Arroita & José J. Lahoz-Monfort, 2017. "Species occupancy estimation and imperfect detection: shall surveys continue after the first detection?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 381-398, October.
    6. Christian H. Weiß & Hee‐Young Kim, 2014. "Diagnosing and modeling extra‐binomial variation for time‐dependent counts," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(5), pages 588-608, September.
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    Cited by:

    1. Yao Kang & Shuhui Wang & Dehui Wang & Fukang Zhu, 2023. "Analysis of zero-and-one inflated bounded count time series with applications to climate and crime data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 34-73, March.

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