In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the asymptotic properties of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset.

翻译：本文提出了一种基于二项稀疏算子与负二项稀疏算子的新型混合整数值门限自回归一阶过程，并讨论了该模型的基本概率与统计性质。推导了条件最小二乘（CLS）与条件最大似然（CML）估计量，建立了估计量的渐近性质。基于CLS与CML得分函数获得了门限参数的推断方法。此外，应用Wald检验以检测分段结构的存在性。进行了模拟研究，并结合实际应用案例：对匹兹堡数据集中刑事恶意破坏事件数量的分析。