Collaborative Research: NSF-SNSF: Tail-robust Analysis of High-dimensional Nonstationary Time Series

High-dimensional time series data arise in many fields such as economics, epidemiology, neuroscience, and social science, where large numbers of measurements are collected over time. These data often exhibit complex patterns, including shifts in behavior and extreme values that violate classical statistical assumptions. This project addresses fundamental challenges in analyzing such time series, especially when they are not stationary and prone to abrupt structural changes. The research in this project aims to develop new methods that are robust to extreme events and better suited to the realities of modern data. By improving the ability to detect and interpret changes in large, evolving systems, this project may be used to support scientific discovery across disciplines. It also provides training opportunities for graduate students, helping build a more data-literate workforce. The project advances the frontiers of science and supports the development of innovative statistical tools that can enhance decision-making in dynamic environments. The research conducted within the scope of this project develops a new tail-robust statistical framework for the analysis of high-dimensional nonstationary time series. The project focuses on two interrelated goals: (1) to construct robust estimators of autocovariance structures that remain accurate in the presence of outliers and large deviations, and (2) to develop efficient procedures to detect and quantify structural changes over time. The investigators plan to address methodological challenges associated with high dimensionality, nonstationarity, and heavy-tailed distributions by integrating techniques from robust statistics, random matrix theory, and change-point analysis. The methods are expected to accommodate piecewise stationary processes with unknown structure changes and offer valid inference in settings where the traditional approaches fail. This work aims to yield powerful data analytic tools for complex time-dependent data and to open new directions in time series modeling, particularly in settings where classical assumptions break down. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.