The segmentation of data into stationary stretches also known as multiple change point problem is important for many applications in time series analysis as well as signal processing. Based on strong invariance principles, we analyse data segmentation methodology using moving sum (MOSUM) statistics for a class of regime-switching multivariate processes where each switch results in a change in the drift. In particular, this framework includes the data segmentation of multivariate partial sum, integrated diffusion and renewal processes even if the distance between change points is sublinear. We study the asymptotic behaviour of the corresponding change point estimators, show consistency and derive the corresponding localisation rates which are minimax optimal in a variety of situations including an unbounded number of changes in Wiener processes with drift. Furthermore, we derive the limit distribution of the change point estimators for local changes - a result that can in principle be used to derive confidence intervals for the change points.

翻译：在时间序列分析和信号处理的许多应用中,将数据分解成固定区域也称为多变点问题,对于时间序列分析和信号处理的许多应用非常重要。根据强烈的变差原则,我们分析数据分解方法,对每个开关导致漂移变化的一组制度性开关多变过程采用移动和(MOSUM)统计法。特别是,这个框架包括多变部分和数据分解、综合扩散和更新过程的数据分解,即使变化点之间的距离是亚线的。我们研究了相应的变化点估计器的静态行为,显示了一致性,并得出了在各种情况下最优化的相应本地化率,包括动态维纳进程无限制的变化数量。此外,我们得出了本地变化的变更点估计器的极限分布,这一结果原则上可用于为变化点获取信任间隔。