High-Dimensional Time Series Segmentation via Factor-Adjusted Vector Autoregressive Modeling

Cho, Haeran; Maeng, Hyeyoung; Eckley, Idris A.; Fearnhead, Paul

Abstract

Vector autoregressive (VAR) models are popularly adopted for modeling high-dimensional time series, and their piecewise extensions allow for structural changes in the data. In VAR modeling, the number of parameters grow quadratically with the dimensionality which necessitates the sparsity assumption in high dimensions. However, it is debatable whether such an assumption is adequate for handling datasets exhibiting strong serial and cross-sectional correlations. We propose a piecewise stationary time series model that simultaneously allows for strong correlations as well as structural changes, where pervasive serial and cross-sectional correlations are accounted for by a time-varying factor structure, and any remaining idiosyncratic dependence between the variables is handled by a piecewise stationary VAR model. We propose an accompanying two-stage data segmentation methodology which fully addresses the challenges arising from the latency of the component processes. Its consistency in estimating both the total number and the locations of the change points in the latent components, is established under conditions considerably more general than those in the existing literature. We demonstrate the competitive performance of the proposed methodology on simulated datasets and an application to U.S. blue chip stocks data. Supplementary materials for this article are available online.

Citation

Cho, H., Maeng, H., Eckley, I. A., & Fearnhead, P. (2024). High-Dimensional Time Series Segmentation via Factor-Adjusted Vector Autoregressive Modeling. Journal of the American Statistical Association, 119(547), 2038-2050. https://doi.org/10.1080/01621459.2023.2240054

• Journal Article Type: Article
• Acceptance Date: Jul 14, 2023
• Online Publication Date: Sep 25, 2023
• Publication Date: 2024
• Deposit Date: Oct 2, 2023
• Publicly Available Date: Oct 2, 2023
• Journal: Journal of the American Statistical Association
• Print ISSN: 0162-1459
• Electronic ISSN: 1537-274X
• Publisher: Taylor and Francis Group
• Peer Reviewed: Peer Reviewed
• Volume: 119
• Issue: 547
• Pages: 2038-2050
• DOI: https://doi.org/10.1080/01621459.2023.2240054
• Keywords: Statistics, Probability and Uncertainty; Statistics and Probability
• Public URL: https://durham-repository.worktribe.com/output/1755463