MOVING SUM DATA SEGMENTATION FOR STOCHASTIC PROCESSES BASED ON INVARIANCE

The segmentation of data into stationary stretches, also known as the multiple change point problem, is important for many applications in time series analysis and signal processing. Based on strong invariance principles, we analyze a data segmentation methodology using moving sum statistics for a class of regimeswitching 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 the change points is sublinear. We study the asymptotic behavior of the corresponding change point estimators, show their consistency, and derive the corresponding localization 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. This result can, in principle, be used to derive confidence intervals for the change points.