A Consistent Characteristic-Function-Based Test for Conditional Independence

This paper proposes a nonparametric test of conditional independence based on the notion that two conditional distributions are equal if and only if the corresponding conditional characteristic functions are equal. We use the functional delta method to expand the test statistic around the population truth and establish asymptotic normality under $\beta -$mixing conditions. We show that the test is consistent and has power against local alternatives at distance $n^{-1/2}h_{1}^{-(d_{1}+d_{3})/4}.$ The cases for which not all random variables of interest are\ continuously valued or observable are also treated, and we show that the test is nuisance-parameter free. Simulation results suggest that the test has better finite sample performance than the Hellinger metric test of Su and White (2002) in detecting nonlinear Granger causality in the mean. Applications to exchange rates and to stock prices and trading volumes indicate that our test can reveal some interesting nonlinear causal relations that the traditional linear Granger causality test fails to detect.