A New Framework for Inference Based on Bilinear Forms of Covariance Estimators of High-Dimensional Time Series and Its Applications

• Applicant: Professor Dr. Ansgar Steland
• Subject Area: Mathematics ; Statistics and Econometrics
• Term: from 2015 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 278220126

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
• Cooperation Partner: Professor Dr. Rainer von Sachs