The Annals of Statistics

Break detection in the covariance structure of multivariate time series models

Alexander Aue, Siegfried Hörmann, Lajos Horváth, and Matthew Reimherr

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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.

Article information

Ann. Statist. Volume 37, Number 6B (2009), 4046-4087.

First available in Project Euclid: 23 October 2009

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Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 91B84: Economic time series analysis [See also 62M10] 60F17: Functional limit theorems; invariance principles

Change-points covariance functional central limit theorem multivariate GARCH models multivariate time series structural breaks


Aue, Alexander; Hörmann, Siegfried; Horváth, Lajos; Reimherr, Matthew. Break detection in the covariance structure of multivariate time series models. Ann. Statist. 37 (2009), no. 6B, 4046--4087. doi:10.1214/09-AOS707.

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