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.

中文翻译：

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自激磁滞负二项式自回归

本文研究了一个以计数为依据的时间序列的观察驱动模型，在该模型中，观察应遵循以过去信息为条件的负二项式分布，并采用滞后自回归的形式。滞后自回归是经典两域​​阈值过程的扩展，具有更灵活的状态切换机制。该模型的稳定性是通过电子链和李雅普诺夫方法建立的。利用基于泊松的得分估计函数通过拟最大似然函数获得回归参数的估计量，并建立了相应的渐近性质。此外，还提出了一种合理的选择阈值搜索范围的方法，并考虑了仿真研究。作为应用，