Joint Structural Break Detection and Parameter Estimation in High-Dimensional Nonstationary VAR Models

• 成果类型: Article
• 署名作者: Safikhani, Abolfazl; Shojaie, Ali
• 署名单位: State University System of Florida; University of Florida; University of Washington; University of Washington Seattle
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1770097
• 发表日期: 2022
• 页码: 251-264
• 关键词: change-point detection; time-series; vector autoregressions; network; Lasso; regularization; covariance

摘要

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to assume piecewise stationarity, where the model can change at potentially many change points. We propose a three-stage procedure for simultaneous estimation of change points and parameters of high-dimensional piecewise vector autoregressive (VAR) models. In the first step, we reformulate the change point detection problem as a high-dimensional variable selection one, and solve it using a penalized least square estimator with a total variation penalty. We show that the penalized estimation method over-estimates the number of change points, and propose a selection criterion to identify the change points. In the last step of our procedure, we estimate the VAR parameters in each of the segments. We prove that the proposed procedure consistently detects the number and location of change points, and provides consistent estimates of VAR parameters. The performance of the method is illustrated through several simulated and real data examples.for this article are available online.