Testing for instability in covariance structures
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 th...
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| Format: | Article |
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Bernoulli Society for Mathematical Statistics and Probability
2017
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| Online Access: | https://eprints.nottingham.ac.uk/46942/ |
| _version_ | 1848797433613516800 |
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| author | Kao, Chihwa Trapani, Lorenzo Urga, Giovanni |
| author_facet | Kao, Chihwa Trapani, Lorenzo Urga, Giovanni |
| author_sort | Kao, Chihwa |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:03:48Z |
| format | Article |
| id | nottingham-46942 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:03:48Z |
| publishDate | 2017 |
| publisher | Bernoulli Society for Mathematical Statistics and Probability |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-469422020-05-04T18:57:06Z https://eprints.nottingham.ac.uk/46942/ Testing for instability in covariance structures Kao, Chihwa Trapani, Lorenzo Urga, Giovanni 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. Bernoulli Society for Mathematical Statistics and Probability 2017-07-27 Article PeerReviewed Kao, Chihwa, Trapani, Lorenzo and Urga, Giovanni (2017) Testing for instability in covariance structures. Bernoulli, 24 (1). pp. 740-771. ISSN 1573-9759 changepoint; covariance matrix; CUSUM statistic; eigensystem https://projecteuclid.org/euclid.bj/1501142461 doi:10.3150/16-BEJ894 doi:10.3150/16-BEJ894 |
| spellingShingle | changepoint; covariance matrix; CUSUM statistic; eigensystem Kao, Chihwa Trapani, Lorenzo Urga, Giovanni Testing for instability in covariance structures |
| title | Testing for instability in covariance structures |
| title_full | Testing for instability in covariance structures |
| title_fullStr | Testing for instability in covariance structures |
| title_full_unstemmed | Testing for instability in covariance structures |
| title_short | Testing for instability in covariance structures |
| title_sort | testing for instability in covariance structures |
| topic | changepoint; covariance matrix; CUSUM statistic; eigensystem |
| url | https://eprints.nottingham.ac.uk/46942/ https://eprints.nottingham.ac.uk/46942/ https://eprints.nottingham.ac.uk/46942/ |