Segmenting time series via self-normalisation

• 成果类型: Article
• 署名作者: Zhao, Zifeng; Jiang, Feiyu; Shao, Xiaofeng
• 署名单位: University of Notre Dame; Fudan University; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12552
• 发表日期: 2022
• 页码: 1699-1725
• 关键词: multiple change-points; binary segmentation; structural-change; number; tests

摘要

We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully non-parametric, robust to temporal dependence and avoids the demanding consistent estimation of long-run variance. 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-normalisation- (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.