LEAPS-MPS: Frequency domain methods for high-dimensional time series

Southern Methodist University, Dallas TX

Investigators

Abstract

High-dimensional time series data are gathered in diverse scientific fields such as economics, social science, neuroscience, and engineering. Modern advancements in data collection technologies, techniques and strategies have led to such datasets being gathered in these fields. As an example, in neuroimaging recent technological developments have given rise to brain signal data recorded across time from several hundred locations in the brain and this results in high-dimensional time series data with highly intricate correlation patterns. As another example energy grid management requires modeling time series data observed from renewable and non-renewable sources from several locations. This project tackles important challenges associated with high-dimensional time series data analysis and will appeal to scientific communities spanning multiple disciplines. Frequency domain theory and methods in this project touch upon new and under-developed areas in statistics, and these methods are uniquely positioned to answer key research questions and generate immediate impact in application areas such as neuroscience, biology, and engineering. Students recruited through this project will benefit from unique opportunities to work on modern day large time series datasets, learn about fundamental linear algebraic methods that are useful in statistics, get exposure to interdisciplinary research and write efficient computer code for handling heavy computations. The investigator will mentor undergraduate and graduate students, assist in enhancing their professional development through interdisciplinary collaborations, and make contributions to increase participation rates among underrepresented groups in mathematics, statistics, and data science. The project includes the development of a new frequency domain modeling framework for a large class of stationary and nonstationary high-dimensional time series. Under this new modeling framework, the investigator will work on building dimension reduction techniques, namely, principal component analysis, factor modeling, and stationary subspace analysis. The computational tractability, under the high-dimensional regime, will be studied along with relevant theoretical justifications. In addition, new multi-frequency autoregressive models that can measure serial and contemporaneous correlations between different oscillatory components of the observed time series will be developed. To validate the new methods, the investigator will carry out extensive simulation studies and apply these new techniques to analyze multiple publicly available high-dimensional time series datasets. With limited existing theoretical advancement concerning frequency domain techniques for high-dimensional time series, the new theoretical results will be of great interest to the time series and statistics communities. This project brings ample scope for interdisciplinary interactions and the investigator will oversee development of user-friendly software packages to make the research easily accessible to researchers in statistics and beyond. 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.