Multiple-change-point detection for high dimensional time series via sparsified binary segmentation

TL;DR

This paper introduces the Sparsified Binary Segmentation (SBS) algorithm for high-dimensional time series segmentation, effectively identifying change-points by thresholding CUSUM statistics to reduce noise impact, supported by a new multivariate Locally Stationary Wavelet model.

Contribution

The paper proposes the SBS algorithm for high-dimensional change-point detection and introduces a multivariate Locally Stationary Wavelet model for theoretical analysis.

Findings

SBS effectively detects change-points in high-dimensional data.

Thresholding improves robustness against noise and sparse changes.

Theoretical consistency of SBS is established under the new wavelet model.

Abstract

Time series segmentation, a.k.a. multiple change-point detection, is a well-established problem. However, few solutions are designed specifically for high-dimensional situations. In this paper, our interest is in segmenting the second-order structure of a high-dimensional time series. In a generic step of a binary segmentation algorithm for multivariate time series, one natural solution is to combine CUSUM statistics obtained from local periodograms and cross-periodograms of the components of the input time series. However, the standard "maximum" and "average" methods for doing so often fail in high dimensions when, for example, the change-points are sparse across the panel or the CUSUM statistics are spuriously large. In this paper, we propose the Sparsified Binary Segmentation (SBS) algorithm which aggregates the CUSUM statistics by adding only those that pass a certain threshold. This "sparsifying" step reduces the impact of irrelevant, noisy contributions, which is particularly beneficial in high dimensions. In order to show the consistency of SBS, we introduce the multivariate Locally Stationary Wavelet model for time series, which is a separate contribution of this work.