Open Access
February 2018 Testing for instability in covariance structures
Chihwa Kao, Lorenzo Trapani, Giovanni Urga
Bernoulli 24(1): 740-771 (February 2018). DOI: 10.3150/16-BEJ894


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.


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Chihwa Kao. Lorenzo Trapani. Giovanni Urga. "Testing for instability in covariance structures." Bernoulli 24 (1) 740 - 771, February 2018.


Received: 1 September 2014; Revised: 1 August 2016; Published: February 2018
First available in Project Euclid: 27 July 2017

zbMATH: 06778346
MathSciNet: MR3706775
Digital Object Identifier: 10.3150/16-BEJ894

Keywords: changepoint , Covariance matrix , CUSUM statistic , eigensystem

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 1 • February 2018
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