Robust change detection in the dependence structure of multivariate time series

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.