AI 中文总结
本研究提出BARBS方法用于非平稳时间序列多变点检测，经数值实验和美国通胀数据分析验证，其稳健性与性能优于现有方法，可准确识别变点。
AI 中文摘要
我们提出了自助辅助稳健二元分割（BARBS），这是一种用于一般非平稳时间动态下多变点检测的递归二元分割方法。针对CUSUM统计量，我们提出了一种新颖的高斯乘子自助法，该方法对复杂的依赖结构具有稳健性。通过对递归各阶段的临界值进行细致校准，BARBS确保在无变点的原假设下控制I类错误。当存在变点时，BARBS以预先指定的概率识别出正确的变点数量，且所得变点位置估计量达到与经典二元分割相同的一致收敛速率。在此基础上，我们引入第二阶段精估计量，该估计量在固定跳跃幅度和消失跳跃幅度下均达到最优的个体定位速率，并确立其渐近分布与近最优一致定位速率。在多种设置下开展的大量数值实验证实，相较于现有方法，BARBS具有稳健性且性能更优。为说明所提方法的实际相关性，我们对美国通胀数据进行分析，所得变点与若干已记录的宏观经济事件相吻合。
英文摘要
We develop bootstrap-assisted robust binary segmentation (BARBS), a recursive binary segmentation method for multiple change point detection under general nonstationary temporal dynamics. A novel Gaussian multiplier bootstrap for the CUSUM statistics is proposed, offering robustness to complex dependence structures. Through meticulous calibration of the critical values at each stage of the recursion, BARBS ensures control of the Type I error under the null hypothesis of no change points. When change points are present, BARBS identifies the correct number of changes with a prespecified probability, and the resulting change point location estimators attain the same uniform consistency rate as classical binary segmentation. Building on this, we introduce second-stage refined estimators that achieve the optimal individual localization rate, and establish their asymptotic distributions and nearly optimal uniform localization rates under both fixed and vanishing jump magnitudes. Extensive numerical experiments across various settings confirm the robustness and superior performance of BARBS relative to existing approaches. To illustrate the practical relevance of the proposed methodology, we analyze U.S. inflation data, yielding change points that align with several documented macroeconomic episodes.
