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Robust Change Detection in the Dependence Structure of Multivariate Time Series

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Abstract

A robust change-point test based on the spatial sign covariance matrix is proposed. A major advantage of the test is its computational simplicity, making it particularly appealing for robust, high-dimensional data analysis. We derive the asymptotic distribution of the test statistic for stationary sequences, which we allow to be near-epoch dependent in probability (P NED) with respect to an α-mixing process. Contrary to the usual L2 near-epoch dependence, this short-range dependence condition requires no moment assumptions, and includes arbitrarily heavy-tailed processes. Further, we give a short review of the spatial sign covariance matrix and compare our test to a similar one based on the sample covariance matrix in a simulation study.

Keywords

GARCH Near epoch dependence Oja sign covariance matrix Orthogonal invariance Spatial sign covariance matrix Tyler matrix 

Notes

Acknowledgements

This work was supported in part by the Collaborative Research Grant 823 of the German Research Foundation.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute for Complex Systems and Mathematical BiologyUniversity of AberdeenAberdeenUK
  2. 2.Fakultät StatistikTechnische Universität DortmundDortmundGermany

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