We apply a three-step sequential procedure to estimate the change-point of count time series. Under certain regularity conditions, the estimator of change-point converges in distribution to the location of the maxima of a two-sided random walk. We derive a closed-form approximating distribution for the maxima of the two-sided random walk based on the invariance principle for the strong mixing processes, so that the statistical inference for the true change-point can be carried out. It is for the first time that such properties are provided for integer-valued time series models. Moreover, we show that the proposed procedure is applicable for the integer-valued autoregressive conditional heteroskedastic (INARCH) models with Poisson or negative binomial conditional distribution. In simulation studies, the proposed procedure is shown to perform well in locating the change-point of INARCH models. And, the procedure is further illustrated with empirical data of weekly robbery counts in two neighborhoods of Baltimore City.

中文翻译：

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一类计数时间序列模型的变化点估计

我们应用三步顺序程序来估计计数时间序列的变化点。在一定的规律性条件下，变化点的估计量在分布上收敛到一个双边随机游走的最大值的位置。我们基于强混合过程的不变性原理推导出了双边随机游走最大值的封闭式逼近分布，从而可以对真实变化点进行统计推断。这是第一次为整数值时间序列模型提供此类属性。此外，我们表明，所提出的程序适用于具有泊松或负二项式条件分布的整数值自回归条件异方差 (INARCH) 模型。在模拟研究中，所提出的程序在定位 INARCH 模型的变化点方面表现良好。并且，通过巴尔的摩市两个街区每周抢劫次数的经验数据进一步说明了该过程。