Plenary Lecture

Models and Procedures for the Analysis of Covariance Matrices of High-Dimensional Time Series

Professor Ansgar Steland
Institute of Statistics
RWTH Aachen University

Abstract: The inferential analysis of the correlation structure of high dimensional vector time series plays an important role in data science and big data. Applications range from sensor data to sparse PCA, shrinkage estimation and risk analysis in portfolio management. The case that a large number d of time series is observed at n time points, where d may be larger than the sample size n, is challenging and has become an active area of statistical research. A common approach is to rely on regularized estimators, for which, however, there is a lack of asymptotic theory which would allow us to construct valid inferential procedures such as hypothesis tests or confidence intervals. We discuss recent results which provide appropriate large sample asymptotics, in the sense of strong or weak approximations by Wiener processes. These results allow us to propose methods for statistical inference and, especially, the detection of change-points where the dependence structure changes. New results on consistent estimation of the change-point are presented as well. It is worth mentioning that known limit theorems dealing with high dimensional data usually work under some constraint on the the dimension d and the sample size n, as in classical random matrix theory. Contrary to this stream of research, the results presented here impose no constraints on d. Specific change-point time series models are discussed, for which the covariance structure changes at an unknown time instant. We investigate in some detail the statistical properties of the proposed change-point test, focusing on the type I error rate (false detection of a change-point) and the statistical power to detect the change-point.

Brief Biography of the Speaker: Ansgar Steland received the M.Sc. and Ph.D. degrees in mathematics from the University of Go╠łttingen, Germany. He held positions as an assistant at the Technical University of Berlin, Berlin, Germany, as a consultant in industry, as a postdoc at the European University Viadrina of Frankfurt/Oder, Germany, and as a lecturer at the Faculty of Mathematics at the Ruhr-University Bochum. Since 2006 he has been a Professor at RWTH Aachen University, Germany, where he holds the Chair of Stochastics at the Institute of Statistics. He is an Elected Member of the International Statistical Institute (ISI) and acts as the chair of the Society for Reliability, Quality and Safety and as the chair of the Section on Statistics in Natural Sciences and Technology of the German Statistical Society. He organized and co-organized several international workshops and invited sessions. His current research interests are in nonparametric statistics, high-dimensional inference, signal and change-point detection, sequential analysis and quality control, empirical processes, time series analysis, econometrics and applications to photovoltaics.

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