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

2025-08-30

AI Summary

Detecting change points in extremal dependence structures of multivariate heavy-tailed time series remains challenging—existing methods either neglect tail characteristics or rely on restrictive parametric assumptions and low-dimensional settings. Method: We propose a nonparametric, multiscale, multi-threshold approach based on moving sums, integrating local bandwidth selection, extremal dependence measures, and an adaptive threshold fusion mechanism. This avoids sensitive global threshold choices inherent in classical extreme-value analysis, accommodates high-dimensional data, and imposes no distributional assumptions. Contribution/Results: The method is theoretically guaranteed to be consistent under weak dependence. Simulation studies demonstrate high accuracy and robustness across diverse dependence and tail scenarios. Applied to neonatal electroencephalogram (EEG) data, it successfully identifies change points in extremal dependence structure despite stationarity in mean and pairwise correlations—validating its effectiveness and unique practical value in real-world biomedical applications.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Detects abrupt changes in multivariate extremal dependence structure
• Addresses threshold selection challenges in multivariate extremes analysis
• Identifies tail dependence changes without correlation shifts

Innovation

• Nonparametric moving sum method
• Multiscale multi-threshold variant approach
• Detects pairwise extremal dependence changes