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The segmentation of data into stationary stretches also known as multiplechange point problem is important for many applications in time series analysisas well as signal processing. Based on strong invariance principles, we analysedata segmentation methodology using moving sum (MOSUM) statistics for a classof regime-switching multivariate processes where each switch results in achange in the drift. In particular, this framework includes the datasegmentation of multivariate partial sum, integrated diffusion and renewalprocesses even if the distance between change points is sublinear. We study theasymptotic behaviour of the corresponding change point estimators, showconsistency and derive the corresponding localisation rates which are minimaxoptimal in a variety of situations including an unbounded number of changes inWiener processes with drift. Furthermore, we derive the limit distribution ofthe change point estimators for local changes - a result that can in principlebe used to derive confidence intervals for the change points.

Moving sum data segmentation for stochastics processes based on invariance