Characteristic Function Based Testing For Conditional Independence: A Nonparametric Regression Approach

We propose a characteristic function based test for conditional independence, which is applicable in both cross-sectional and time series contexts. Our test is not only asymptotically locally more powerful than Su and White’s (2007) test, but also is more flexible in inferring patterns of conditional dependence. In addition to our ominous test, we also propose a class of derivative tests to gauge possible patterns of conditional dependence. These derivative tests deliver some interesting model-free tests for such important hypotheses as omitted variables, Granger causality in mean and conditional uncorrelatedness. All proposed tests have a convenient asymptotic N(0, 1) distribution under the null hypotheses. Unlike many other smoothed nonparametric tests for conditional independence, we allow nonparametric estimators for both conditional joint and marginal characteristic functions to jointly determine the asymptotic distribution of our tests. This leads to a much better size performance in finite samples. Monte Carlo studies demonstrate the well behavior of our tests in finite samples. In an application to testing nonlinear Granger causality, we document the existence of nonlinear relationships between money and output, which may be ignored by the linear Granger causality test and Su and White’s (2007) test.