A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE

We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f ~ y6 x, z! and f ~ y6x!, which is identically zero under the null+ We use the functional delta method to expand the test statistic around the population value and establish asymptotic normality under b-mixing conditions+ We show that the test is consistent and has power against alternatives at distance n 102h d04+ The cases for which not all random variables of interest are continuously valued or observable are also discussed+ Monte Carlo simulation results indicate that the test behaves reasonably well in finite samples and significantly outperforms some earlier tests for a variety of data generating processes+ We apply our procedure to test for Granger noncausality in exchange rates+