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

## TL;DR

This paper introduces a nonparametric, joint bivariate method for detecting change points in both expectation and variance of univariate data sequences, improving inference over univariate methods.

## Contribution

It proposes a novel bivariate moving sum approach for joint detection of changes in mean and variance, supported by a multi-scale analysis and theoretical validation.

## Key findings

- Effective detection of change points in expectation and variance.
- Improved inference accuracy compared to univariate methods.
- Validated through theoretical analysis and simulations.

## 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 as compared to 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 multi-scale 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.