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Title: Testing and estimation of change-points in covariance matrices based on weighted CUSUMs in high-dimensions Authors:  Ansgar Steland - University Aachen (Germany) [presenting]
Abstract: The analysis of high-dimensional covariance matrices of time series is a challenging statistical problem. We approach the problem to test for the presence of a change-point in a sequence of covariance matrices by studying procedures based on weighted CUSUM statistics associated to bilinear forms of the sample covariance matrix. Asymptotic results in terms of strong and weak approximations as well as functional central limit theorems are presented under a change-point time series model. We consider a linear time series framework which allows for approximate VARMA models and a class of spiked covariance models. Further, the results cover approximations for a multivariate CUSUM transform based on L pairs of projection vectors. Consistent estimators for the asymptotic variances and covariances of the weighted CUSUM statistics are considered. Studying sequential versions of these estimators allows us to consider a stopped-sample estimator which uses the data up to the estimated change point. The finite sample properties are investigated by simulations. Lastly, the methods are illustrated by analyzing environmental data.