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Self-excited hysteretic negative binomial autoregression

Author

Listed:
  • Mengya Liu

    (Jilin University)

  • Qi Li

    (Changchun Normal University)

  • Fukang Zhu

    (Jilin University)

Abstract

This paper studies an observation-driven model for time series of counts, in which the observations are supposed to follow a negative binomial distribution conditioned on past information with the form of the hysteretic autoregression. As an extension of the classical two-regime threshold process, the hysteretic autoregression enjoys a more flexible regime-switching mechanism. Stability properties of the model are established by the e-chain and Lyapunov’s method. The estimator for regression parameters is obtained by the quasi-maximum likelihood with Poisson-based score estimating function, and the corresponding asymptotic properties are established. Moreover, a reasonable method for selecting search ranges for thresholds is also proposed and simulation studies are considered. As an application, we bring attention to some features of the daily number of trades of Siparex Croissance which have been overlooked in previous studies.

Suggested Citation

  • Mengya Liu & Qi Li & Fukang Zhu, 2020. "Self-excited hysteretic negative binomial autoregression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 385-415, September.
    • Handle: RePEc:spr:alstar:v:104:y:2020:i:3:d:10.1007_s10182-019-00360-6
    DOI: 10.1007/s10182-019-00360-6
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    2. 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.

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