A Bootstrap Causality Test for Covariance Stationary Processes

This paper examines a nonparametric test for Granger-causality for a vector covariance stationary linear process under, possibly, the presence of long-range dependence. We show that the test converges to a non-distribution free multivariate Gaussian process, say vec (B(amp;#956;)) indexed by amp;#956; amp;#1028; [0,1]. Because, contrary to the scalar situation, it is not possible, except in very specific cases, to find a time transformation g(amp;#956;) such that vec (B(g(amp;#956;))) is a vector with independent Brownian motion components, it implies that inferences based on vec (B(amp;#956;)) will be difficult to implement. To circumvent this problem, we propose bootstrapping the test by two alternative, although similar, algorithms showing their validity and consistency