A new statistic and practical guidelines for nonparametric Granger causality testing
Upon illustrating how smoothing may cause over-rejection in nonparametric tests for Granger non-causality, we propose a new test statistic for which problems of this type can be avoided. We develop asymptotic theory for the new test statistic, and perform a simulation study to investigate the properties of the new test in comparison with its natural counterpart, the Hiemstra-Jones test. Our simulation results indicate that, if the bandwidth tends to zero at the appropriate rate as the sample size increases, the size of the new test remains close to nominal, while the power remains large. Transforming the time series to uniform marginals improves the behavior of both tests. In applications to Standard and Poor's index volumes and returns, the Hiemstra-Jones test suggests that volume Granger-causes returns. However, the evidence for this gets weaker if we carefully apply the recommendations suggested by our simulation study.
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