Nonlinear Granger Causality: Guidelines for Multivariate Analysis

In this paper we propose an extension of the nonparametric Granger causality test, originally introduced by Diks and Panchenko [2006. A new statistic and practical guidelines for nonparametric Granger causality testing. Journal of Economic Dynamics \& Control 30, 1647-1669]. We show that the basic test statistics lacks consistency in the multivariate setting. The problem is the result of the kernel density estimator bias, which does not converge to zero at a sufficiently fast rate when the number of conditioning variables is larger than one. In order to overcome this difficulty we apply the data-sharpening method for bias reduction. We then derive the asymptotic properties of the `sharpened' test statistics and we investigate its performance numerically. We conclude with an empirical application to the US grain market.