Assessment of Resampling Methods for Causality Testing

Different resampling methods for the null hypothesis of non-causality are assessed. As test statistic the partial transfer entropy (PTE), an information and model-free measure, is used. Two resampling techniques, 1) the time shifted surrogates and 2) the stationary bootstrap, are combined with the following three independence settings (giving in total six resampling schemes), all consistent to the null hypothesis of non-causality: A) only the driving variable is resampled, B) both the driving and response variable are independently resampled, and C) both the driving and response variable are resampled while also the dependence of the future of the response variable and the vector of its past values is destroyed. The empirical null distribution of the PTE as the surrogate and bootstrapped time series become more independent is examined along with the size and power of the respective tests. Further, we consider the resampling method of contemporaneously resampling the the driving and the response time series using the stationary bootstrap. Although this resampling method does not comply with the non-causality hypothesis, one can obtain an accurate sampling distribution of the mean of the test statistic since the mean value of the test statistic is zero under H0. This resampling scheme performs well in terms of size and power, provided that the null distribution of the bootstrap values of the test statistic is shifted to have mean zero.