Open Access
December 2009 Break detection in the covariance structure of multivariate time series models
Alexander Aue, Siegfried Hörmann, Lajos Horváth, Matthew Reimherr
Ann. Statist. 37(6B): 4046-4087 (December 2009). DOI: 10.1214/09-AOS707


In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to many of the multivariate GARCH models established in the literature, and also works well in the case of high dimensionality of the underlying data. Since it is nonparametric, the procedure avoids the difficulties associated with parametric model selection, model fitting and parameter estimation. We provide the theoretical foundation for the test and demonstrate its applicability via a simulation study and an analysis of financial data. Extensions to multiple changes and the case of infinite fourth moments are also discussed.


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Alexander Aue. Siegfried Hörmann. Lajos Horváth. Matthew Reimherr. "Break detection in the covariance structure of multivariate time series models." Ann. Statist. 37 (6B) 4046 - 4087, December 2009.


Published: December 2009
First available in Project Euclid: 23 October 2009

zbMATH: 1191.62143
MathSciNet: MR2572452
Digital Object Identifier: 10.1214/09-AOS707

Primary: 60K35 , 62M10
Secondary: 60F17 , 91B84

Keywords: Change-points , Covariance , functional central limit theorem , multivariate GARCH models , multivariate time series , structural breaks

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6B • December 2009
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