Cui Yunwei, Wu Rongning, Zheng Qi
Department of Mathematics, Towson University, Towson, Maryland, USA.
Zicklin School of Business, Baruch College, The City University of New York, New York, New York, USA.
Scand Stat Theory Appl. 2021 Dec;48(4):1277-1313. doi: 10.1111/sjos.12489. Epub 2020 Aug 25.
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.
我们应用一种三步序贯程序来估计计数时间序列的变化点。在某些正则性条件下，变化点的估计量依分布收敛到双边随机游走最大值的位置。基于强混合过程的不变性原理，我们推导出双边随机游走最大值的闭式近似分布，从而可以对真实变化点进行统计推断。对于整数值时间序列模型，首次给出了此类性质。此外，我们表明所提出的程序适用于具有泊松或负二项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，该程序通过巴尔的摩市两个街区每周抢劫次数的实证数据进一步说明。
