Bivariate change point detection: Joint detection of changes in expectation and variance

Abstract

A method for change point detection is proposed. We consider a univariate sequence of independent random variables with piecewise constant expectation and variance, apart from which the distribution may vary periodically. We aim to detect change points in both expectation and variance. For that, we propose a statistical test for the null hypothesis of no change points and an algorithm for change point detection. Both are based on a bivariate moving sum approach that jointly evaluates the mean and the empirical variance. The joint consideration helps improve inference compared with separate univariate approaches. We infer on the strength and the type of changes with confidence. Nonparametric methodology supports the analysis of diverse data. Additionally, a multiscale approach addresses complex patterns in change points and effects. We demonstrate the performance through theoretical results and simulation studies. A companion R-package jcp (available on CRAN) is discussed.

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

“…But note that h too large may result in overlap of subsequent changes and thus in an estimation bias. In order to account for change points that occur on multiple time scales, including rapid changes as well as small effects, methods that combine multiple windows were proposed, see e.g., Messer (2019); Cho and Kirch (2020). They work in two steps: first change point candidates are generated for every single h, and afterwards all sets are merged giving final estimates.…”