In this article, we introduce a new random coefficients self-exciting threshold integer-valued autoregressive process. The autoregressive coefficients are driven by a logistic regression structure, so that the explanatory variables can be included. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators, as well as the asymptotic properties of the estimators, are discussed. The nonlinearity test of the model and existence test of explanatory variables are also addressed. As an illustration, we evaluate our estimates through a simulation study. Finally, we apply our method to the data sets of sexual offences in Ballina, New South Wales (NSW), Australia, with two covariates of temperature and drug offences. The result reveals that the proposed model fits the data sets well.

在本文中，我们介绍了一种新的随机系数自激阈值整数值自回归过程。自回归系数由逻辑回归结构驱动，因此可以包含解释变量。讨论了该模型的基本概率和统计性质。讨论了条件最小二乘和条件最大似然估计器，以及这些估计器的渐近性质。还讨论了模型的非线性检验和解释变量的存在检验。作为说明，我们通过模拟研究评估我们的估计。最后，我们将我们的方法应用于带有温度和毒品犯罪的两个协变量的澳大利亚新南威尔士州巴利纳的性犯罪数据集。