Localised pruning for data segmentation based on multiscale change point procedures
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The segmentation of a time series into piecewise stationary segments is an important problem both in time series analysis and signal processing. It requires the estimation of the total number of change points, which amounts to a model selection problem, as well as their locations. Many algorithms exist for the detection and estimation of multiple change points in the mean of univariate data, from those that find a global minimiser of an information criterion, to multiscale methods that achieve good adaptivity in the localisation of change points via multiple scanning of the data. For the latter, the problem of duplicate or false positives needs to be addressed, for which we propose a localised application of Schwarz information criterion. As a generic methodology, this new approach is applicable with any multiscale change point methods fulfilling mild assumptions to prune down the set of candidate change point estimators. We establish the theoretical consistency of the proposed localised pruning method in estimating the number and locations of multiple change points under general conditions permitting heavy tails and dependence. In particular, we show that it achieves minimax optimality in change point localisation in combination with a multiscale extension of the moving sum-based procedure when there are a finite number of change points. Extensive simulation studies and real data applications confirm good numerical performance of the proposed methodology.
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