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Analysis of zero-and-one inflated bounded count time series with applications to climate and crime data

Author

Listed:
  • Yao Kang

    (Xi’an Jiaotong University)

  • Shuhui Wang

    (Jilin University)

  • Dehui Wang

    (Liaoning University)

  • Fukang Zhu

    (Jilin University)

Abstract

This article introduces a new version of first-order binomial autoregressive (BAR(1)) process with zero-and-one inflated binomial marginals using the idea of hidden Markov models, which contains the BAR(1) and other existing processes as special cases. Stochastic properties of the new model are investigated and model parameters are estimated by the probability-based, quasi-maximum likelihood, maximum likelihood and Bayesian methods. A binomial one-inflation index is constructed and further utilized to develop a method to test whether zero and/or one inflation with respect to a BAR(1) model. We also give the asymptotic distribution of the corresponding test statistics under the null hypothesis. Applications to rainy-days and assaults-on-officers counts are conducted, which shows that the proposed model can accurately capture zero-inflation, one-inflation and overdispersion characteristics of the data. The predictive distributions are employed to identify the occurrence of anomalies and then establish early warning system of risk.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:1:d:10.1007_s11749-022-00825-y
    DOI: 10.1007/s11749-022-00825-y
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    References listed on IDEAS

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    1. 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.
    2. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
    3. 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.
    4. Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.
    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. Raju Maiti & Atanu Biswas & Bibhas Chakraborty, 2018. "Modelling of low count heavy tailed time series data consisting large number of zeros and ones," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 407-435, August.
    7. 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.
    8. 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.
    9. 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.
    10. Huaping Chen & Qi Li & Fukang Zhu, 2021. "Binomial AR(1) processes with innovational outliers," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(2), pages 446-472, January.
    11. Christian H. Weiß & Philip K. Pollett, 2012. "Chain Binomial Models and Binomial Autoregressive Processes," Biometrics, The International Biometric Society, vol. 68(3), pages 815-824, September.
    12. Mengya Liu & Fukang Zhu & Ke Zhu, 2022. "Modeling normalcy‐dominant ordinal time series: An application to air quality level," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 460-478, May.
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