B0904
Title: Change points in dependence structures of weak and strong dependent high-dimensional time series
Authors: Ansgar Steland - RWTH Aachen University (Germany) [presenting]
Abstract: For high-dimensional vector time series of dimension $d=d_n$ depending on the sample size $n$, the case that $d$ is large compared to $n$ or is even larger than $n$ is of particular interest. We are interest to construct change-point statistics for such high-dimensional time series, in order to investigate the dependence structure for changes. The proposed test can also be used to study changes in linear projections of high-dimensional data. Within a high-dimensional time series model that allows for full covariance matrices, we propose novel large sample approximations for bilinear forms of the sample variance-covariance matrix, in terms of strong approximations by Brownian motions. The results cover weakly as well as many long-range dependent linear processes and are valid for a large class of projection vectors that arise, naturally or by construction, in many statistical problems extensively studied for high-dimensional vector time series. Among those key applications are sparse financial portfolio optimization and sparse principal component analysis. Our results are also directly applicable to the problem of shrinkage estimation. The large sample approximations finally allow us to propose a high-dimensional change-point analysis, in order to test for the presence of a change-point in the dependence structure.
