AN EXTENDED VERSION OF SIMS' NONCAUSALITY IN MULTIPLE TIME SERIES AND ITS TEST STATISTIC

Abstract

An extended version of Sims' noncausality is presented on partitioned subvectors of multiple time series. It is shown that this is not equivalent to “generalized” Granger's noncausality in multiple time series. The necessary and sufficient condition for both Granger's instantaneous noncausality and the extended version of Sims' noncausality to be held is that block matrices of the MA representation are zero. A statistic for testing noncausality is given and its asymptotic distribution is chi-square distribution with the degree of freedom of the numbers of components of a subvector. An expression of relative power contribution in multiple time series is introduced in view of noncausality test.