Modeling Temporal Dynamics of Large Systems from High-Dimensional Time Series Data

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The answers to many questions in the biological and social sciences require understanding how the components of a large system dynamically interact with each other and give rise to emergent behavior. For instance, simultaneous failure of a handful of small but highly-connected firms can lead to huge systemic losses in the financial system. Interactions among neurophysiological signals in different brain regions relate to the organization of human brain connectome. This project aims to develop rigorous and computationally efficient statistical methods to jointly model the temporal dynamics of such large systems using high-dimensional time series datasets. These methods will enable researchers to gain deeper insights into the structure of these systems and help with more accurate data-driven decision making. It is anticipated that the methods under development can be used in clinical neuroscience to search for functional connectivity patterns associated with neurological disorders, and in financial regulation for monitoring systemic risk and identifying systemically important firms in the financial systems.Specifically, this project will focus on two classes of estimation and inference problems in high-dimensional time series: (i) developing novel theory and methods for estimating high-dimensional spectral density and coherence matrices, which can be viewed as a natural generalization of covariance and correlation matrix estimation problems to high-dimensional time series, and (ii) developing novel theoretical machinery to quantify uncertainty (confidence intervals and hypothesis tests) in high-dimensional vector autoregressive models. Broadly speaking, the research will attempt to bridge a gap between current frontiers of high-dimensional statistics for independent data and time series data using tools from disciplines including optimization, statistics, signal processing, and random matrix theory. This intellectual unification of ideas may provide novel insights in deciphering the workings of complex systems in a data-driven fashion.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.