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

在时间序列中，大数据通常是指高维时间序列（HDTS）。与单独分析单个序列不同，重点是构建一个单一框架，以同时从许多相互依赖的变量的时间序列中学习。HDTS统计和机器学习方法的进步吸引了各个领域的经济学家、金融分析师、工程师和科学家的极大关注。该项目旨在为HDTS开发新的统计模型、推理工具和理论，同时探索它们与深度学习的接口。通过跨学科和合作研究，以及在不同学术水平的课程开发和指导方面的努力，将促进这项研究对科学界和社会的更广泛影响。这个项目有三个主要目标。第一个目标是开发比现有模型更灵活、计算可扩展和/或可解释的新HDTS模型，同时填补高维有限阶和无限阶矢量自回归框架之间的关键空白。第二个目标是开发易于实现的推理工具，以及严谨的理论和高效的算法，通过混合最先进的理论和HDTS建模和张量学习的技术，可以解决HDTS分析中的经验重要目标，如格兰杰因果关系检验和动态因素推理。第三个目标是探索和利用HDTS模型和递归神经网络（RNN）之间的内在联系，为基于非线性深度学习的HDTS模型开发新的算法和统计理论。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.