Joint Structural Break Detection and Parameter Estimation in High-Dimensional Nonstationary VAR Models. Issue 537 (2nd January 2022)

• Record Type: Journal Article
• Authors: Safikhani, Abolfazl; Shojaie, Ali
• Is Part Of: Journal of the American Statistical Association. Volume 117:Issue 537(2022)
• Page Start: 251
• Page End: 264
• Publication Date: 2022-01-02
• Subjects: High-dimensional time series -- Piecewise stationarity -- Structural breaks -- Total variation penalty; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2020.1770097
• Languages: English
• ISSNs: 0162-1459

Abstract

Abstract: 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. Supplementary materials for this article are available online.