Segmenting Time Series via Self-Normalization

TL;DR

This paper introduces a versatile, fully nonparametric change-point detection method for multivariate time series that is robust, easy to tune, and applicable to various parameters like mean, variance, and correlation.

Contribution

It develops a novel self-normalization based framework combined with a nested local-window segmentation algorithm for broad and robust change-point detection.

Findings

Effective in detecting multiple change-points across different parameters.

Outperforms existing methods in numerical experiments.

Applicable to real-world multivariate time series data.

Abstract

We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. One salient and distinct feature of the proposed method is its versatility, where it allows change-point detection for a broad class of parameters (such as mean, variance, correlation and quantile) in a unified fashion. At the core of our method, we couple the self-normalization (SN) based tests with a novel nested local-window segmentation algorithm, which seems new in the growing literature of change-point analysis. Due to the presence of an inconsistent long-run variance estimator in the SN test, non-standard theoretical arguments are further developed to derive the consistency and convergence rate of the proposed SN-based change-point detection method. Extensive numerical experiments and relevant real data analysis are conducted to illustrate the effectiveness and broad applicability of our proposed method in comparison with state-of-the-art approaches in the literature.