High-Dimensional Time-Series Models With Time-Dependent Coefficients

• Applicant: Professor Dr. Johannes Lederer
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 573018111

Time-series analysis is one of the core topics in statistics. But the high dimensionality and sheer size of many current datasets confront the field with new statistical and algorithmic challenges. At the same time, traditional questions like stability and stationarity remain highly relevant. This project tries to approach those new challenges and some of the traditional questions simultaneously. We place ourselves in a high-dimensional, time-varying, autoregressive modeling setup. The starting point for estimating the coefficients is then the standard least-squares estimator, but we complement that estimator with innovative regularization and calibration schemes, and we equip the resulting methods with algorithms and statistical guarantees by interweaving concepts from high-dimensional statistics, convex optimization, and classical time-series analysis. Thus, more generally speaking, our project tries to take a step forward in broadening and modernizing the theoretical and applied scope of time-series analysis.

• DFG Programme: Research Grants