A Bootstrap Causality Test for Covariance Stationary Processes.

摘要

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 nondistribution free multivariate Gaussian process, say vec(B-tilde(mu)) indexed by mu is a member of [0,1]. Because, contrary to the scalar situation, it is not possible, except in very specific cases, to find a time transformation g(mu) such that vec(B-tilde(g(mu))) is a vector with independent Brownian motion components, it implies that inferences based on vec(B-tilde(mu)) will be difficult to implement. To circumvent this problem, we propose to bootstrapping the test by two alternative, although similar, algorithms showing their validity and consistency.