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The segmentation of a time series into piecewise stationary segments, a.k.a.multiple change point analysis, is an important problem both in time seriesanalysis and signal processing. In the presence of multiscale change pointswith both large jumps over short intervals and small changes over longstationary intervals, multiscale methods achieve good adaptivity in theirlocalisation but at the same time, require the removal of false positives andduplicate estimators via a model selection step. In this paper, we propose alocalised application of Schwarz information criterion which, as a genericmethodology, is applicable with any multiscale candidate generating procedurefulfilling mild assumptions. We establish the theoretical consistency of theproposed localised pruning method in estimating the number and locations ofmultiple change points under general assumptions permitting heavy tails anddependence. Further, we show that combined with a MOSUM-based candidategenerating procedure, it attains minimax optimality in terms of detection lowerbound and localisation for i.i.d. sub-Gaussian errors. A careful comparisonwith the existing methods by means of (a) theoretical properties such asgenerality, optimality and algorithmic complexity, (b) performance on simulateddatasets and run time, as well as (c) performance on real data applications,confirm the overall competitiveness of the proposed methodology.

Two-stage data segmentation permitting multiscale change points, heavy tails and dependence