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An integer-valued threshold autoregressive process based on negative binomial thinning

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Abstract

In this paper, we introduce an integer-valued threshold autoregressive process, which is driven by independent negative-binomial distributed random variables and based on negative binomial thinning. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators and corresponding iterative algorithms are investigated for both the cases that the threshold variable is known or not. Also, the asymptotic properties of the estimators are obtained. Finally, some numerical results of the estimates and a real data example are presented.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (No. 11271155, 11371168, J1310022, 11571138, 11501241, 11571051), Science and Technology Research Program of Education Department in Jilin Province for the 12th Five-Year Plan (440020031139) and Jilin Province Natural Science Foundation (20130101066JC, 20130522102JH, 20150520053JH).

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Authors and Affiliations

  1. Institute of Mathematics Jilin University, Changchun, Jilin, 130012, People’s Republic of China

    Kai Yang, Dehui Wang & Han Li

  2. School of Statistics Jilin University of Finance and Economics, Changchun, Jilin, 130117, People’s Republic of China

    Boting Jia

Authors
  1. Kai Yang
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  2. Dehui Wang
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  3. Boting Jia
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  4. Han Li
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Correspondence to Dehui Wang.

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Yang, K., Wang, D., Jia, B. et al. An integer-valued threshold autoregressive process based on negative binomial thinning. Stat Papers 59, 1131–1160 (2018). https://doi.org/10.1007/s00362-016-0808-1

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