Optimal rank-based tests for block exogeneity in vector autoregressions

The aim of this paper is to construct a class of locally asymptotically most stringent (in the Le Cam sense) tests for independence between two sets of variables in the V AR models. These tests are based on multivariate ranks of distances and multivariate signs of the observations and are shown to be asymptotically distribution-free under very mild assumptions on the noise, which is obtained by applying a linear transformation to marginally spherical innovations. The class of tests derived is invariant with respect to the group of block affine transformations and asymptotically invariant with respect to the group of continuous monotone marginal radial transformations.