Barnett et al. in 2009 proved that Granger causality and transfer en-tropy causality measure are equivalent for time series which have a Gaussian distribution. Granger causality test is linear, while transfer entropy a non-linear test. Many biological and physical mechanisms show to have non-Gaussian distributions. In this paper we investigate under which conditions on probability density distributions of the data can the equivalence of the two causality measures be extended. In the complexity sense ”cheaper” linear Granger test can be applied for detection of causality in time series satisfying these conditions. These results have an impact on causality detection in common biological and physical time series.

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