Advances in High-dimensional Time Series Modeling and Its Interface with Deep Learning

In time series, big data typically refer to high-dimensional time series (HDTS). Instead of analyzing individual series separately, the focus is on building a single framework to learn from time series of many interdependent variables simultaneously. Advances in statistical and machine learning methods for HDTS have attracted enormous attention from economists, financial analysts, engineers, and scientists in various fields. This project aims to develop new statistical models, inference tools and theory for HDTS while also exploring their interface with deep learning. The broader impact of this research on scientific communities and society will be promoted through interdisciplinary and collaborative research as well as efforts in course development and mentoring at different academic levels. This project has three main objectives. The first objective is to develop new HDTS models that are more flexible, computationally scalable, and/or interpretable than existing ones, while filling the critical gap between finite- and infinite-order vector autoregressive frameworks in high dimensions. The second objective is to develop easy-to-implement inference tools, along with rigorous theory and efficient algorithms, that can address empirically important goals in HDTS analysis, such as Granger causality tests and dynamic factor inference, by blending state-of-the-art theory and techniques from HDTS modeling and tensor learning. The third objective is to explore and exploit the intrinsic connection between HDTS models and recurrent neural networks (RNN) to develop new algorithms and statistical theory for nonlinear deep learning-based HDTS models. 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.