A new method for detecting non-linear causality in time series

In this work, we propose a new non-parametric method to identify non-linear causality between time series. Indeed, we detect non-linear causality when the moments or higher-order statistics of the underlying probability distribution of the effect time series depends instantaneously on the cause time series. The analysis of simulated data and empirical financial time series shows that our method is very accurate and superior to non-linear Granger causality method.