Nonparametric Copula-Based Test for Conditional Independence with Applications to Granger Causality

Abstract

This article proposes a new nonparametric test for conditional independence that can directly be applied to test for Granger causality. Based on the comparison of copula densities, the test is easy to implement because it does not involve a weighting function in the test statistic, and it can be applied in general settings since there is no restriction on the dimension of the time series data. In fact, to apply the test, only a bandwidth is needed for the nonparametric copula. We prove that the test statistic is asymptotically pivotal under the null hypothesis, establishes local power properties, and motivates the validity of the bootstrap technique that we use in finite sample settings. A simulation study illustrates the size and power properties of the test. We illustrate the practical relevance of our test by considering two empirical applications where we examine the Granger noncausality between financial variables. In a first application and contrary to the general findings in the literature, we provide evidence on two alternative mechanisms of nonlinear interaction between returns and volatilities: nonlinear leverage and volatility feedback effects. This can help better understand the well known asymmetric volatility phenomenon. In a second application, we investigate the Granger causality between stock index returns and trading volume. We find convincing evidence of linear and nonlinear feedback effects from stock returns to volume, but a weak evidence of nonlinear feedback effect from volume to stock returns.