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

Hee-Young Kim, Christian H. Weiß () and Tobias A. Möller
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Hee-Young Kim: Korea University
Christian H. Weiß: Helmut Schmidt University
Tobias A. Möller: Helmut Schmidt University

Statistical Methods & Applications, 2018, vol. 27, issue 4, No 14, 689-714

Abstract: 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.

Keywords: Binomial AR(1) model; Binomial index of dispersion; Binomial zero index; Extra-binomial dispersion; Extra-binomial zeros; Adjusted sample size; 62M10; 62F03 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10260-018-00431-z

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