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Keywords:

  • VAR models;
  • contemporaneous non-correlation;
  • instantaneous causality;
  • elliptical densities;
  • multivariate ranks;
  • signs

The aim of this paper was to test for contemporaneous non-causality defined by Granger (1969) between two groups of variables in a VAR(p) setting. Since contemporaneous correlation of the innovations is a necessary condition for contemporaneous causality (Pierce and Haugh, 1977), we focused on testing some restrictions on the covariance matrix of the noise. The class of the derived tests is locally asymptotically most stringent (in the Le Cam sense), invariant with respect to the group of block affine transformations and asymptotically invariant with respect to the group of continuous monotone radial transformations. Those tests are based on multivariate ranks of distances and multivariate signs of the o bservations and are shown to be asymptotically distribution free under very mild assumptions on the noise.