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

Abstract

A method for change point detection is proposed. In a sequence of independent and piecewise identically distributed random variables we aim at detecting both, changes in the expectation as well as changes in the variance. We propose a statistical test for the null hypothesis of the absence of change points, and an algorithm for change point detection. For that we exploit the joint dynamics of the mean and the empirical variance in the context of bivariate moving sum statistics. The joint consideration helps to improve change point inference as compared to separate univariate approaches. We infer on the effects, i.e., on the strength and the type of the changes, with confidence. Non-parametric methodology allows for a high variety of data to be analyzed. A multi-scale aspect addresses the detection of complex patterns in change points and effects. We demonstrate the performance through theoretical results and simulations studies. A companion R-package jcp (available on CRAN) is discussed.