Publication: A nonparametric copula based test for conditional independence with applications to granger causality
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2009-06
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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
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Nonparametric tests, Conditional independence, Granger non-causality, Bernstein density copula, Bootstrap, Finance, Volatility asymmetry, Leverage effect, Volatility feedback effect, Macroeconomics