Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection\u2014rejoinder

Piotr Fryzlewicz

doi:10.1007/s42952-020-00085-2

Abstract

Many existing procedures for detecting multiple change-points in data sequences fail in frequent-change-point scenarios. This article proposes a new change-point detection methodology designed to work well in both infrequent and frequent change-point settings. It is made up of two ingredients: one is “Wild Binary Segmentation 2” (WBS2), a recursive algorithm for producing what we call a ‘complete’ solution path to the change-point detection problem, i.e. a sequence of estimated nested models containing 0, ldots , T-1 change-points, where T is the data length. The other ingredient is a new model selection procedure, referred to as “Steepest Drop to Low Levels” (SDLL). The SDLL criterion acts on the WBS2 solution path, and, unlike many existing model selection procedures for change-point problems, it is not penalty-based, and only uses thresholding as a certain discrete secondary check. The resulting WBS2.SDLL procedure, combining both ingredients, is shown to be consistent, and to significantly outperform the competition in the frequent change-point scenarios tested. WBS2.SDLL is fast, easy to code and does not require the choice of a window or span parameter.

Highlights

I would like to start by thanking all sets of discussants: Moulinath Banerjee; Haeran Cho and Claudia Kirch; Solt Kovács, Housen Li and Peter Bühlmann; Robert Lund
Does Wild Binary Segmentation 2” (WBS2).Steepest Drop to Low Levels” (SDLL) work for theoretically small spacings between changepoints? Both Banerjee and Cho and Kirch raise the issue of whether WBS2.SDLL works for settings in which spacings between change-points are o(T), in addition to the O(T) case discussed in the paper
WBS2.SDLL is advertised as a procedure that works well in frequent change-point scenarios, so should not we expect this to be reflected in the fact that it permits o(T) spacings?

Summary

Introduction

I would like to start by thanking all sets of discussants: Moulinath Banerjee; Haeran Cho and Claudia Kirch; Solt Kovács, Housen Li and Peter Bühlmann; Robert Lund. Both Banerjee and Cho and Kirch raise the issue of whether WBS2.SDLL works for settings in which spacings between change-points are o(T), in addition to the O(T) case discussed in the paper.

Results

Conclusion