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

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