and

This paper proposes a simple consistent nonparametric test of conditional symmetry based on the principle of characteristic functions. The test statistic is shown to be asymptotically normal under the null hypothesis of conditional symmetry and consistent against any conditional asymmetric distributions. We also study the power against local alternatives, propose a bootstrap version of the test, and conduct a small Monte Carlo simulation to evaluate the finite-sample performance of the test. c © 2005 Peking University Pres