# MOPED: A moving sum method for change point detection in pairwise extremal dependence

## TL;DR

This paper introduces MOPED, a nonparametric method for detecting multiple change points in the extremal dependence structure of multivariate data, effectively identifying subtle tail dependence changes without parametric assumptions.

## Contribution

The paper presents a novel multiscale, multi-threshold extension of MOPED that improves change point detection in extremal dependence, applicable to complex multivariate time series.

## Key findings

- MOPED accurately detects change points in tail dependence in simulations.
- The method identifies subtle extremal dependence changes in EEG data.
- MOPED outperforms existing approaches in nonparametric tail dependence analysis.

## Abstract

It is increasingly the case with modern time series that many data sets of practical interest contain abrupt changes in structure. These changes may occur in complex characteristics such as the extremal dependence structure, and identifying such structural breaks remains a challenging problem. Many existing change point detection algorithms focus on changes in dependence across the entire distribution, rather than the tails, and approaches that are tailored to extremes typically make strict parametric assumptions or they are only applicable to bivariate data. We propose a nonparametric MOving sum-based approach for detecting multiple changes in the Pairwise Extremal Dependence (MOPED) of multivariate regularly varying data. To avoid the classical problem of threshold selection in the study of multivariate extremes, we further propose a multiscale, multi-threshold variant of MOPED that pools change point estimates across choices of the threshold and the bandwidth used in local estimation. Good performance of MOPED is illustrated in a simulation study, and we showcase its ability to identify subtle changes in tail dependence class in the absence of correlation changes. We further demonstrate the usefulness of MOPED by identifying changes in the extremal connectivity of electroencephalogram (EEG) signals of seizure-prone neonates.