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In this paper, we introduce an asymptotic test procedure to assess thestability of volatilities and cross-volatilites of linear and nonlinearmultivariate time series models. The test is very flexible as it can beapplied, for example, to many of the multivariate GARCH models established inthe literature, and also works well in the case of high dimensionality of theunderlying data. Since it is nonparametric, the procedure avoids thedifficulties associated with parametric model selection, model fitting andparameter estimation. We provide the theoretical foundation for the test anddemonstrate its applicability via a simulation study and an analysis offinancial data. Extensions to multiple changes and the case of infinite fourthmoments are also discussed.

Break detection in the covariance structure of multivariate time series models