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Diagnosing and modeling extra‐binomial variation for time‐dependent counts

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  • Christian H. Weiß
  • Hee‐Young Kim

Abstract

This article considers the modeling of count data time series with a finite range having extra‐binomial variation. We propose a beta‐binomial autoregressive model using the concept of random coefficient thinning. We discuss the stationarity conditions, derive the moments and autocovariance function and consider approaches for parameter estimation. Furthermore, we develop two new tests for detecting extra‐binomial variation, and we derive the asymptotic distributions of the test statistics under the null hypothesis of a binomial autoregressive model. The size and power performance of the two tests are analyzed under various alternatives taken from a beta‐binomial autoregressive model with Monte Carlo experiments. The article ends with a real‐data example about the Harmonised Index of Consumer Prices of the European Union. Copyright © 2013 John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:apsmbi:v:30:y:2014:i:5:p:588-608
    DOI: 10.1002/asmb.2005
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    Cited by:

    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. Huaping Chen & Qi Li & Fukang Zhu, 2022. "A new class of integer-valued GARCH models for time series of bounded counts with extra-binomial variation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 243-270, June.
    3. Christian H. Weiß, 2017. "On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 997-1007, September.
    4. 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.

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