Segmenting time series via self‐normalisation

Zifeng Zhao, Feiyu Jiang and Xiaofeng Shao

Journal of the Royal Statistical Society Series B, 2022, vol. 84, issue 5, 1699-1725

Abstract: 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.

Date: 2022
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