Sequential testing for structural stability in approximate factor models

Barigozzi, Matteo; Trapani, Lorenzo

Abstract

We develop a monitoring procedure to detect changes in a large approximate factor model. Letting r be the number of common factors, we base our statistics on the fact that the(r + 1)-th eigenvalue of the sample covariance matrix is bounded under the null of no change, whereas it becomes spiked under changes. Given that sample eigenvalues cannot be estimated consistently under the null, we randomise the test statistic, obtaining a sequence of i.i.d statistics, which are used for the monitoring scheme. Numerical evidence shows a very small probability of false detections, and tight detection times of change-points.

Citation

Barigozzi, M., & Trapani, L. (2020). Sequential testing for structural stability in approximate factor models. Stochastic Processes and their Applications, 130(8), 5149-5187. https://doi.org/10.1016/j.spa.2020.03.003

• Journal Article Type: Article
• Acceptance Date: Mar 5, 2020
• Online Publication Date: Mar 13, 2020
• Publication Date: 2020-08
• Deposit Date: Mar 13, 2020
• Publicly Available Date: Mar 14, 2021
• Journal: Stochastic Processes and their Applications
• Print ISSN: 0304-4149
• Electronic ISSN: 1879-209X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 130
• Issue: 8
• Pages: 5149-5187
• DOI: https://doi.org/10.1016/j.spa.2020.03.003
• Keywords: large factor model, change-point, sequential testing, randomised tests
• Public URL: https://nottingham-repository.worktribe.com/output/4136739
• Publisher URL: https://www.sciencedirect.com/science/article/abs/pii/S0304414919300031