Detecting departures from meta-ellipticity for multivariate stationary time series

A test for detecting departures from meta-ellipticity for multivariate stationary time series is proposed. The large sample behavior of the test statistic is shown to depend in a complicated way on the underlying copula as well as on the serial dependence. Valid asymptotic critical values are obtained by a bootstrap device based on subsampling. The finite-sample performance of the test is investigated in a large-scale simulation study, and the theoretical results are illustrated by a case study involving financial log returns.