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This paper studies methods for testing and estimating change-points in thecovariance structure of a high-dimensional linear time series. The assumedframework allows for a large class of multivariate linear processes (includingvector autoregressive moving average (VARMA) models) of growing dimension andspiked covariance models. The approach uses bilinear forms of the centered ornon-centered sample variance-covariance matrix. Change-point testing andestimation are based on maximally selected weighted cumulated sum (CUSUM)statistics. Large sample approximations under a change-point regime areprovided including a multivariate CUSUM transform of increasing dimension. Forthe unknown asymptotic variance and covariance parameters associated to (pairsof) CUSUM statistics we propose consistent estimators. Based on weak laws oflarge numbers for their sequential versions, we also consider stopped sampleestimation where observations until the estimated change-point are used. Finitesample properties of the procedures are investigated by simulations and theirapplication is illustrated by analyzing a real data set from environmetrics.

Testing and Estimating Change-Points in the Covariance Matrix of a High-Dimensional Time Series