The segmentation of a time series into piecewise stationary segments is an important problem both in time series analysis and signal processing. In the presence of multiscale change points with both large jumps over short intervals and small jumps over long intervals, multiscale methods achieve good adaptivity but require a model selection step for removing false positives and duplicate estimators. We propose a localised application of the Schwarz criterion, which is applicable with any multiscale candidate generating procedure fulfilling mild assumptions, and establish its theoretical consistency in estimating the number and locations of multiple change points under general assumptions permitting heavy tails and dependence. In particular, combined with a MOSUM-based candidate generating procedure, it attains minimax rate optimality in both detection lower bound and localisation for i.i.d. sub-Gaussian errors. Overall competitiveness of the proposed methodology compared to existing methods is shown through its theoretical and numerical performance.

将时间序列分割成分段平稳段是时间序列分析和信号处理中的一个重要问题。在存在短间隔大跳跃和长间隔小跳跃的多尺度变化点的情况下，多尺度方法实现了良好的适应性，但需要模型选择步骤来消除误报和重复估计量。我们提出了 Schwarz 准则的局部应用，该准则适用于满足温和假设的任何多尺度候选生成程序，并在允许重尾和依赖性的一般假设下估计多个变化点的数量和位置时建立其理论一致性。特别是，结合基于 MOSUM 的候选生成程序，它在 iid 亚高斯误差的检测下界和定位方面都达到了极小极大速率的最优性。与现有方法相比，所提出的方法的整体竞争力通过其理论和数值表现得以体现。