  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.
