The project aims at establishing and further developing a comprehensive methodology for large-sample approximations of bilinear forms of covariance matrix estimators of high-dimensional time series as well as elaborating on its applications to statistical inference. It is intended to derive approximations by (functionals) of Gaussian processes for a large class of time series going beyond the framework of factor models without assuming conditions on the dimension. The results will be used to study both classical fixed sample procedures, such as confidence intervals to quantify uncertainty, and sequential methods, especially change-point tests and sequential detectors. As a well-established class of regularized covariance estimators shrinkage methods will be investigated. Further, the general results will be used and extended to study multivariate tests within a high-dimensional time series framework.
DFG Programme
Research Grants
International Connection
Belgium
