Multiple Change Point Detection in Reduced Rank High Dimensional Vector Autoregressive Models

• 成果类型: Article
• 署名作者: Bai, Peiliang; Safikhani, Abolfazl; Michailidis, George
• 署名单位: State University System of Florida; University of Florida; State University System of Florida; University of Florida; State University System of Florida; University of Florida
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2079514
• 发表日期: 2023
• 页码: 2776-2792
• 关键词: principal stratification; Causal Inference; outcomes; Identifiability; identification; Mediation

摘要

We study the problem of detecting and locating change points in high-dimensional Vector Autoregressive (VAR) models, whose transition matrices exhibit low rank plus sparse structure. We first address the problem of detecting a single change point using an exhaustive search algorithm and establish a finite sample error bound for its accuracy. Next, we extend the results to the case of multiple change points that can grow as a function of the sample size. Their detection is based on a two-step algorithm, wherein the first step, an exhaustive search for a candidate change point is employed for overlapping windows, and subsequently a backward elimination procedure is used to screen out redundant candidates. The two-step strategy yields consistent estimates of the number and the locations of the change points. To reduce computation cost, we also investigate conditions under which a surrogate VAR model with a weakly sparse transition matrix can accurately estimate the change points and their locations for data generated by the original model. This work also addresses and resolves a number of novel technical challenges posed by the nature of the VAR models under consideration. The effectiveness of the proposed algorithms and methodology is illustrated on both synthetic and two real datasets. for this article are available online.