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A new integer-valued threshold autoregressive process based on modified negative binomial operator driven by explanatory variables

Author

Listed:
  • Yixuan Fan

    (Jilin University)

  • Jianhua Cheng

    (Jilin University)

  • Dehui Wang

    (Liaoning University)

Abstract

In this article, a new random coefficient integer-valued self-exciting threshold autoregressive process based on modified negative binomial operator is introduced. The autoregressive coefficients are driven by the explanatory variables via a logistic regression structure. Basic probabilistic and statistical properties of this process are discussed. Estimators of the unknown parameters are obtained via the conditional least squares and conditional maximum likelihood methods, as well as the asymptotic properties. The nonlinearity test of the proposed model and the existence test of explanatory variables are performed using the Wald-type test. Monte Carlo simulations are provided to illustrate the finite-sample performance of the estimators and the hypothesis tests. A real example is applied to illustrate the superiority of the proposed model.

Suggested Citation

  • Yixuan Fan & Jianhua Cheng & Dehui Wang, 2024. "A new integer-valued threshold autoregressive process based on modified negative binomial operator driven by explanatory variables," Statistical Papers, Springer, vol. 65(9), pages 5873-5901, December.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:9:d:10.1007_s00362-024-01605-6
    DOI: 10.1007/s00362-024-01605-6
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    References listed on IDEAS

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    1. Kai Yang & Dehui Wang & Boting Jia & Han Li, 2018. "An integer-valued threshold autoregressive process based on negative binomial thinning," Statistical Papers, Springer, vol. 59(3), pages 1131-1160, September.
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    4. Kai Yang & Han Li & Dehui Wang & Chenhui Zhang, 2021. "Random coefficients integer-valued threshold autoregressive processes driven by logistic regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 533-557, December.
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    8. Huaping Chen & Fukang Zhu & Xiufang Liu, 2022. "A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors," Stats, MDPI, vol. 5(3), pages 1-22, August.
    9. Kai Yang & Yiwei Zhao & Han Li & Dehui Wang, 2023. "On bivariate threshold Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 931-963, November.
    10. 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.
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    13. 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.
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