Multiscale change point detection via gradual bandwidth adjustment in moving sum processes

Abstract

A method for the detection of changes in the expectation in univariate sequences is provided. Moving sum processes (MOSUM) are studied. These rely on the selection of a tuning bandwidth. Here, a framework to overcome bandwidth selection is presented – the bandwidth adjusts gradually. For that, MOSUM are made dependent on both time and the bandwidth: the domain becomes a triangle. On the triangle, paths are constructed which systematically lead to change points. An algorithm is provided that estimates change points by subsequent consideration of paths. Strong consistency for the number and location of change points is shown. Simulation studies corroborate estimation precision and reveal competitiveness with state of the art change point detection methods. A companion $\mathtt{\text{R}}$-package mscp is made available on CRAN.