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

Break detection in the covariance structure of multivariate time series models. (English) Zbl 1191.62143

Ann. Stat. 37, No. 6B, 4046-4087 (2009).
Summary: 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.

Cited in 108 Documents

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60F17 Functional limit theorems; invariance principles
62P05 Applications of statistics to actuarial sciences and financial mathematics
62G10 Nonparametric hypothesis testing
91G70 Statistical methods; risk measures
65C60 Computational problems in statistics (MSC2010)
62G20 Asymptotic properties of nonparametric inference

Keywords:

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

Software:

FinTS
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\textit{A. Aue} et al., Ann. Stat. 37, No. 6B, 4046--4087 (2009; Zbl 1191.62143)
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References:

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