Evidence for existence of real causality in the case of zero Granger causality

Granger causality is one of the most popular measures to reveal causality influence of time series and has been widely applied in economics and neuroscience due to its simplicity and easy implementation. In this paper, we first introduce two key assumptions which are showed to be pre-required for defining Granger causality; that is, without the two assumptions, one cannot draw a conclusion that there is no real causality even if we derive zero Granger causality. We then discuss two cases for which Granger causality is zero but there exists real causality between two time series. Therefore, researchers must be caution in drawing any conclusion based on Granger causality value.