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

TL;DR

This paper introduces a novel multiscale change point detection method that adaptively adjusts bandwidths in moving sum processes, improving detection accuracy and consistency in univariate sequences.

Contribution

It presents a new framework with a gradually adjusting bandwidth for change point detection, along with an algorithm and theoretical consistency results.

Findings

Strong consistency in change point estimation demonstrated

Simulation results show high estimation precision

R-package mscp available on CRAN for implementation

Abstract

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.