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Title: Change detection and estimation for the covariance matrices of a high-dimensional time series Authors:  Ansgar Steland - University Aachen (Germany) [presenting]
Abstract: New results about inference and change point analysis of zero mean high dimensional vector time series are discussed. Applications cover sparse principal component analyses, financial portfolio management and signal processing. The results deal with change-point procedures that can be based on an increasing number of bilinear forms of the sample variance-covariance matrix as arising, for instance, when studying change-in-variance problems for projection statistics and shrinkage covariance matrix estimation. Contrary to many known results, e.g. from random matrix theory, the results hold true without any constraint on the dimension, the sample size or their ratio. The large sample approximations are in terms of (strong resp. weak) approximations by Gaussian processes. They hold not only without any constraint on the dimension, the sample size or their ratios, but even without any such constraint with respect to the number of bilinear form. Further, distributional approximations for shrinkage covariance matrix estimators are provided including a confidence interval for the shrinkage intensity and lower and upper bounds for the covariance matrix. These bounds lead to novel bounds for portfolio risks in financial portfolio analysis. The accuracy of the methods is investigated by simulations. Lastly, we discuss an application to asset returns from financial markets.