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

Abstract

This paper proposes a new nonparametric test for conditional independence, which is based on the comparison of Bernstein copula densities using the Hellinger distance. 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 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, establish local power properties, and motivate the validity of the bootstrap technique that we use in finite sample settings. A simulation study illustrates the good size and power properties of the test. We illustrate the empirical relevance of our test by focusing on Granger causality using financial time series data to test for nonlinear leverage versus volatility feedback effects and to test for causality between stock returns and trading volume. In a third application, we investigate Granger causality between macroeconomic variables. JEL Classification: C12; C14; C15; C19; G1; G12; E3; E4; E52.

The Testing of Causal Stock Returns-Trading Volume Dependencies with the Aid of Copulas

“…The contributors draw the conclusion that trading volume can be used to obtain more precise estimates of daily volatility for cases in which high-frequency returns are unavailable. Bouezmarni et al [12] derived a nonparametric test based on Bernstein copulas and tested on the basis of high frequency data for causality between stock returns and trading volume. The contributors proved, that at a 5% significance level, the nonparametric test rejected clearly the null hypothesis of non-causality from returns to volume, which is in line with the conclusion which followed from the linear test.…”

“…The contributors applied their test to examine Granger non-causality in exchange rates. These drawbacks were addressed by Bouezmarni et al [12]. We use their approach and methodology in the empirical part of this paper.…”

“…Next for k = ⎢ ⎣ ⎥ ⎦ = 2 1000 63 the density function*, was estimated by means of a nonparametric estimator based on binomial distributions. Bouezmarni et al [12] focus on the differences between their test (called hereafter the BRT test) and the test by Su and White [43]. The main differences (and advantages of the BRT test) can be summarized as follows:…”

“…The authors applied their test in an examination Granger non-causality between many macroeconomic and financial variables. [12]):…”

“…They take into account the fact that the densities of the variables are conditional. This method was applied by Bouezmarni et al [12] and Su and White [43] 1. In the first step X t * is generated by means of the kernel estimator: …”