### 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

Original language | English |
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Title of host publication | Modern Nonparametric, Robust and Multivariate Methods |

Subtitle of host publication | Festschrift in Honour of Hannu Oja |

Editors | Klaus Nordhausen, Sara Taskinen |

Publisher | Springer International Publishing |

Pages | 265-288 |

Number of pages | 24 |

ISBN (Electronic) | 978-3-319-22404-6 |

ISBN (Print) | 978-3-319-22403-9 |

DOIs | |

Publication status | Published - 2015 |

### Keywords

- GARCH
- near epoch dependence
- Oja sign covariance matrix
- orthogonal invariance
- spatial sign covariance matrix
- Tyler matrix

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## Cite this

Vogel, D., & Fried, R. (2015). (5) Robust change detection in the dependence structure of multivariate time series. In K. Nordhausen, & S. Taskinen (Eds.),

*Modern Nonparametric, Robust and Multivariate Methods: Festschrift in Honour of Hannu Oja*(pp. 265-288). Springer International Publishing. https://doi.org/10.1007/978-3-319-22404-6_16