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A new class of integer-valued GARCH models for time series of bounded counts with extra-binomial variation

Author

Listed:
  • Huaping Chen

    (Henan University)

  • Qi Li

    (Changchun Normal University)

  • Fukang Zhu

    (Jilin University)

Abstract

This article considers a modeling problem of integer-valued time series of bounded counts in which the binomial index of dispersion of the observations is greater than one, i.e., the observations inhere the characteristic of extra-binomial variation. Most methods analyzing such characteristic are based on the conditional mean process instead of the observed process itself. To fill this gap, we introduce a new class of beta-binomial integer-valued GARCH models, establish the geometric moment contracting property of its conditional mean process, discuss the stationarity and ergodicity of the observed process and its conditional mean process, and give some stochastic properties of them. We consider the conditional maximum likelihood estimates and establish the asymptotic properties of the estimators. The performances of these estimators are compared via simulation studies. Finally, we apply the proposed models to two real data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:2:d:10.1007_s10182-021-00414-8
    DOI: 10.1007/s10182-021-00414-8
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    Cited by:

    1. Weiß, Christian H. & Zhu, Fukang, 2024. "Conditional-mean multiplicative operator models for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    2. Huaping Chen, 2023. "A New Soft-Clipping Discrete Beta GARCH Model and Its Application on Measles Infection," Stats, MDPI, vol. 6(1), pages 1-19, February.
    3. Huaping Chen & Qi Li & Fukang Zhu, 2023. "A covariate-driven beta-binomial integer-valued GARCH model for bounded counts with an application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 805-826, October.
    4. Zhang, Rui, 2024. "Asymmetric beta-binomial GARCH models for time series with bounded support," Applied Mathematics and Computation, Elsevier, vol. 470(C).

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