Bayes multivariate signification tests and Granger causality

The Granger causality test is reduced, after co-integration, to the test of the fact that some coefficients of linear regressions are equal to zero or not. In this paper we will build multi-variate Bayes tests for the signification of the parameters of linear regression provided by the above Granger causality, instead of using the classical F statistics. We will consider the cases of known variance, respectively unknown variance. Because we replace in practice the Student tests by the Z tests if the involved number of degrees of freedom is at least 30, we can replace in our paper the case of unknown variance with that of known variance, if the above number of degrees of freedom is at least 30.