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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Main Authors:	Kao, Chihwa, Trapani, Lorenzo, Urga, Giovanni
Format:	Article
Language:	English
Published:	Bernoulli Society for Mathematical Statistics and Probability 2017
Online Access:	http://eprints.nottingham.ac.uk/46942/ http://eprints.nottingham.ac.uk/46942/ http://eprints.nottingham.ac.uk/46942/ http://eprints.nottingham.ac.uk/46942/1/BEJ894.pdf

id	nottingham-46942
recordtype	eprints
spelling	nottingham-469422017-10-14T08:48:20Z http://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 application/pdf en http://eprints.nottingham.ac.uk/46942/1/BEJ894.pdf Kao, Chihwa and Trapani, Lorenzo and Urga, Giovanni (2017) Testing for instability in covariance structures. Bernoulli, 24 (1). pp. 740-771. ISSN 1573-9759 https://projecteuclid.org/euclid.bj/1501142461 doi:10.3150/16-BEJ894 doi:10.3150/16-BEJ894
repository_type	Digital Repository
institution_category	Local University
institution	University of Nottingham Malaysia Campus
building	Nottingham Research Data Repository
collection	Online Access
language	English
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.
format	Article
author	Kao, Chihwa Trapani, Lorenzo Urga, Giovanni
spellingShingle	Kao, Chihwa Trapani, Lorenzo Urga, Giovanni Testing for instability in covariance structures
author_facet	Kao, Chihwa Trapani, Lorenzo Urga, Giovanni
author_sort	Kao, Chihwa
title	Testing for instability in covariance structures
title_short	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_sort	testing for instability in covariance structures
publisher	Bernoulli Society for Mathematical Statistics and Probability
publishDate	2017
url	http://eprints.nottingham.ac.uk/46942/ http://eprints.nottingham.ac.uk/46942/ http://eprints.nottingham.ac.uk/46942/ http://eprints.nottingham.ac.uk/46942/1/BEJ894.pdf
first_indexed	2018-09-06T13:49:59Z
last_indexed	2018-09-06T13:49:59Z
_version_	1610866281584525312

Testing for instability in covariance structures

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