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

The segmentation of a time series into piecewise stationary segments is an important problem both in analysis and signal processing. In the presence multiscale change points with large jumps over short intervals small long intervals, methods achieve good adaptivity but require model selection step for removing false positives duplicate estimators. We propose localised application Schwarz criterion, which applicable any candidate generating procedure fulfilling mild assumptions, establish its theoretical consistency estimating number locations multiple under general assumptions permitting heavy tails dependence. particular, combined MOSUM-based procedure, it attains minimax rate optimality detection lower bound localisation i.i.d. sub-Gaussian errors. Overall competitiveness proposed methodology compared to existing shown through numerical performance.