Testing and estimating change-points in the covariance matrix of a high-dimensional time series

JOURNAL OF MULTIVARIATE ANALYSIS

卷:177

Article

Steland, Ansgar¹ 

[1] Rhein Westfal TH Aachen, Inst Stat, D-52065 Aachen, Germany

关键词: Change-point;    CUSUM transform;    Data science;    High-dimensional statistics;    Projection;    Spatial statistics;    Spiked covariance;    Strong approximation;    VARMA processes;   

DOI  :  10.1016/j.jmva.2019.104582

来源: Elsevier

【 摘 要 】

This paper studies methods for testing and estimating change-points in the covariance structure of a high-dimensional linear time series. The assumed framework allows for a large class of multivariate linear processes (including vector autoregressive moving average (VARMA) models) of growing dimension and spiked covariance models. The approach uses bilinear forms of the centered or non-centered sample variance-covariance matrix. Change-point testing and estimation are based on maximally selected weighted cumulated sum (CUSUM) statistics. Large sample approximations under a change-point regime are provided including a multivariate CUSUM transform of increasing dimension. For the unknown asymptotic variance and covariance parameters associated to (pairs of) CUSUM statistics we propose consistent estimators. Based on weak laws of large numbers for their sequential versions, we also consider stopped sample estimation where observations until the estimated change-point are used. Finite sample properties of the procedures are investigated by simulations and their application is illustrated by analyzing a real data set from environmetrics. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free