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(y vertical bar x, z) and f(y vertical bar x), 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 beta-mixing conditions. We show that the test is consistent and has power against alternatives at distance n(-1/2)h(-d/4). 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.