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

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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.

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Acknowledgements

We are very grateful to the AE and anonymous referees for providing several constructive and helpful comments which led to a significant improvement of the paper. Kang is supported by National Natural Science Foundation of China (NSFC) (No. 12101485) and China Postdoctoral Science Foundation (No. 2021M702624). Wang is supported by NSFC (Nos. 11871028 and 11731015). Zhu is supported by NSFC (Nos. 11871027 and 11731015) and Natural Science Foundation of Jilin Province (No. 20210101143JC).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China

    Yao Kang

  2. School of Mathematics, Jilin University, Changchun, China

    Shuhui Wang & Fukang Zhu

  3. School of Mathematics and Statistics, Liaoning University, Shenyang, China

    Dehui Wang

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  1. Yao Kang
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  2. Shuhui Wang
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  3. Dehui Wang
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  4. Fukang Zhu
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Correspondence to Fukang Zhu.

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Kang, Y., Wang, S., Wang, D. et al. Analysis of zero-and-one inflated bounded count time series with applications to climate and crime data. TEST 32, 34–73 (2023). https://doi.org/10.1007/s11749-022-00825-y

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