Hierarchical Change-Point Detection for Multivariate Time Series via a Ball Detection Function

TL;DR

This paper introduces a novel hierarchical change-point detection method using a Ball detection function for multivariate and non-Euclidean time series, capable of identifying multiple change points without prior assumptions.

Contribution

The paper proposes a new Ball detection function and a hierarchical algorithm for consistent change-point detection in dependent, non-linear, and non-Euclidean sequences.

Findings

Method outperforms existing techniques in non-Euclidean data.

Accurately detects multiple change points without prior info.

Effective in real datasets like wind direction and Bitcoin prices.

Abstract

Sequences of random objects arise from many real applications, including high throughput omic data and functional imaging data. Those sequences are usually dependent, non-linear, or even Non-Euclidean, and an important problem is change-point detection in such dependent sequences in Banach spaces or metric spaces. The problem usually requires the accurate inference for not only whether changes might have occurred but also the locations of the changes when they did occur. To this end, we first introduce a Ball detection function and show that it reaches its maximum at the change-point if a sequence has only one change point. Furthermore, we propose a consistent estimator of Ball detection function based on which we develop a hierarchical algorithm to detect all possible change points. We prove that the estimated change-point locations are consistent. Our procedure can estimate the number of change-points and detect their locations without assuming any particular types of change-points as a change can occur in a sequence in different ways. Extensive simulation studies and analyses of two interesting real datasets wind direction and Bitcoin price demonstrate that our method has considerable advantages over existing competitors, especially when data are non-Euclidean or when there are distributional changes in the variance.