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A new INAR(1) process with bounded support for counts showing equidispersion, underdispersion and overdispersion

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Listed:
  • Yao Kang

    (Jilin University)

  • Dehui Wang

    (Jilin University)

  • Kai Yang

    (Changchun University of Technology)

Abstract

The present work introduces a mixture INAR(1) model based on the mixing Pegram and binomial thinning operators with a finite range $$\{0,1,\ldots ,n\}$$ { 0 , 1 , … , n } . The new model can be used to handle equidispersion, underdispersion, overdispersion, zero-inflation and multimodality. Several probabilistic and statistical properties are explored. Estimators of the model parameters are derived by the conditional maximum likelihood method. The asymptotic properties and numerical results of the estimators are also studied. In addition, the forecasting problem is addressed. Applications to real data sets are given to show the application of the new model.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:2:d:10.1007_s00362-019-01111-0
    DOI: 10.1007/s00362-019-01111-0
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    References listed on IDEAS

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    7. Han Li & Kai Yang & Shishun Zhao & Dehui Wang, 2018. "First-order random coefficients integer-valued threshold autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 305-331, July.
    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. Christian Weiß & Hee-Young Kim, 2013. "Parameter estimation for binomial AR(1) models with applications in finance and industry," Statistical Papers, Springer, vol. 54(3), pages 563-590, August.
    10. Mansour Aghababaei Jazi & Geoff Jones & Chin-Diew Lai, 2012. "First-order integer valued AR processes with zero inflated poisson innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(6), pages 954-963, November.
    11. 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.
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