The first-order binomial autoregressive (BAR(1)) model is the most frequently used tool to analyze the bounded count time series. The BAR(1) model is stationary and assumes process parameters to remain constant throughout the time period, which may be incompatible with the non-stationary real data, which indicates piecewise stationary characteristic. To better analyze the non-stationary bounded count time series, this article introduces the BAR(1) process with multiple change-points, which contains the BAR(1) model as a special case. Our primary goals are not only to detect the change-points, but also to give a solution to estimate the number and locations of the change-points. For this, the cumulative sum (CUSUM) test and minimum description length (MDL) principle are employed to deal with the testing and estimation problems. The proposed approaches are also applied to analysis of the Harmonised Index of Consumer Prices of the European Union.

翻译：一阶二项自回归（BAR(1)）模型是分析有界计数时间序列最常用的工具。BAR(1)模型具有平稳性，并假设过程参数在整个时间段内保持不变，但这可能与呈现分段平稳特征的非平稳真实数据不兼容。为更好地分析非平稳有界计数时间序列，本文引入了包含多个变化点的BAR(1)过程，其中BAR(1)模型作为其特例。我们的主要目标不仅是检测变化点，还要给出估计变化点数量及位置的解决方案。为此，采用累积和（CUSUM）检验与最小描述长度（MDL）准则分别处理检验与估计问题。所提出的方法还被应用于欧盟调和消费者价格指数的分析。