High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition

• 成果类型: Article
• 署名作者: Wang, Di; Zheng, Yao; Lian, Heng; Li, Guodong
• 署名单位: University of Hong Kong; University of Connecticut; City University of Hong Kong
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1855183
• 发表日期: 2022
• 页码: 1338-1356
• 关键词: reduced-rank regression; MOVING AVERAGE MODELS; reduction; shrinkage; selection; number

摘要

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This article proposes to rearrange the transition matrices of the model into a tensor form such that the parameter space can be restricted along three directions simultaneously via tensor decomposition. In contrast, the reduced-rank regression method can restrict the parameter space in only one direction. Besides achieving substantial dimension reduction, the proposed model is interpretable from the factor modeling perspective. Moreover, to handle high-dimensional time series, this article considers imposing sparsity on factor matrices to improve the model interpretability and estimation efficiency, which leads to a sparsity-inducing estimator. For the low-dimensional case, we derive asymptotic properties of the proposed least squares estimator and introduce an alternating least squares algorithm. For the high-dimensional case, we establish nonasymptotic properties of the sparsity-inducing estimator and propose an ADMM algorithm for regularized estimation. Simulation experiments and a real data example demonstrate the advantages of the proposed approach over various existing methods. for this article are available online.