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

A method for the detection of changes in the expectation in univariate sequences is provided. Moving sum processes 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, moving sum processes 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. Simulations support estimation precision. A companion R-package mscp is made available on CRAN.