Testing for instability in covariance structures

Kao, Chihwa; Trapani, Lorenzo; Urga, Giovanni

Abstract

We propose a test for the stability over time of the covariance matrix of multivariate time series. The analysis is extended to the eigensystem to ascertain changes due to instability in the eigenvalues and/or eigenvectors. Using strong Invariance Principles and Law of Large Numbers, we normalise the CUSUM-type statistics to calculate their supremum over the whole sample. The power properties of the test versus alternative hypotheses, including also the case of breaks close to the beginning/end of sample are investigated theoretically and via simulation. We extend our theory to test for the stability of the covariance matrix of a multivariate regression model. The testing procedures are illustrated by studying the stability of the principal components of the term structure of 18 US interest rates.

Citation

Kao, C., Trapani, L., & Urga, G. (in press). Testing for instability in covariance structures. Bernoulli, 24(1), https://doi.org/10.3150/16-BEJ894

• Journal Article Type: Article
• Acceptance Date: Aug 26, 2016
• Online Publication Date: Jul 27, 2017
• Deposit Date: Oct 3, 2017
• Publicly Available Date: Oct 3, 2017
• Journal: Bernoulli
• Print ISSN: 1350-7265
• Electronic ISSN: 1573-9759
• Publisher: Bernoulli Society for Mathematical Statistics and Probability
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 1
• DOI: https://doi.org/10.3150/16-BEJ894
• Keywords: changepoint; covariance matrix; CUSUM statistic; eigensystem
• Public URL: https://nottingham-repository.worktribe.com/output/874295
• Publisher URL: https://projecteuclid.org/euclid.bj/1501142461
• Contract Date: Oct 3, 2017