A structural break test for extremal dependence in β-mixing random vectors

Abstract

We derive a structural break test for extremal dependence in β -mixing, possibly high-dimensional random vectors with either asymptotically dependent or asymptotically independent components. Existing tests require serially independent observations with asymptotically dependent components. To avoid estimating a long-run variance, we use self-normalization, which obviates the need to estimate the coefficient of tail dependence when components are asymptotically independent. Simulations show favourable empirical size and power of the test, which we apply to S&P 500 and DAX log-returns. We find evidence for one break in the coefficient of tail dependence for the upper and lower joint tail at the beginning of the 2007–08 financial crisis, leading to more extremal co-movement.