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

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