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Binomial Autoregressive Processes With Density-Dependent Thinning

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  • Christian H. Weiß
  • Philip K. Pollett

Abstract

type="main" xml:id="jtsa12054-abs-0001"> We present an elaboration of the usual binomial AR(1) process on {0,1, … ,N}that allows the thinning probabilities to depend on the current state N only through the ‘density’ n ∕ N, a natural assumption in many real contexts. We derive some basic properties of the model and explore approaches to parameter estimation. Some special cases are considered that allow for overdispersion and underdispersion, as well as positive and negative autocorrelations. We derive a law of large numbers and a central limit theorem, which provide useful large-N approximations for various quantities of interest.

Suggested Citation

  • Christian H. Weiß & Philip K. Pollett, 2014. "Binomial Autoregressive Processes With Density-Dependent Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 115-132, March.
    • Handle: RePEc:bla:jtsera:v:35:y:2014:i:2:p:115-132
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    File URL: http://hdl.handle.net/10.1002/jtsa.12054
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    Citations

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    Cited by:

    1. Annika Homburg & Christian H. Weiß & Layth C. Alwan & Gabriel Frahm & Rainer Göb, 2019. "Evaluating Approximate Point Forecasting of Count Processes," Econometrics, MDPI, vol. 7(3), pages 1-28, July.
    2. Han Li & Zijian Liu & Kai Yang & Xiaogang Dong & Wenshan Wang, 2024. "A pth-order random coefficients mixed binomial autoregressive process with explanatory variables," Computational Statistics, Springer, vol. 39(5), pages 2581-2604, July.
    3. Ángel López-Oriona & José A. Vilar, 2023. "Ordinal Time Series Analysis with the R Package otsfeatures," Mathematics, MDPI, vol. 11(11), pages 1-23, June.
    4. 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.
    5. Yao Kang & Dehui Wang & Kai Yang, 2021. "A new INAR(1) process with bounded support for counts showing equidispersion, underdispersion and overdispersion," Statistical Papers, Springer, vol. 62(2), pages 745-767, April.
    6. 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.
    7. 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.
    8. 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.
    9. William Kengne, 2023. "On consistency for time series model selection," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 437-458, July.
    10. 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.
    11. Zhang, Rui, 2024. "Asymmetric beta-binomial GARCH models for time series with bounded support," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    12. Tobias A. Möller & Maria Eduarda Silva & Christian H. Weiß & Manuel G. Scotto & Isabel Pereira, 2016. "Self-exciting threshold binomial autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 369-400, October.
    13. Christian Weiß, 2015. "A Poisson INAR(1) model with serially dependent innovations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 829-851, October.
    14. 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.

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