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Testing for instability in covariance structures

Kao, Chihwa; Trapani, Lorenzo; Urga, Giovanni

Authors

Chihwa Kao

Giovanni Urga



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 http://eprints.nottingham.ac.uk/id/eprint/46942
Publisher URL https://projecteuclid.org/euclid.bj/1501142461
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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