Information-theoretic generalization of Granger causality principle, based on evaluation of conditional mutual information, also known as transfer entropy (CMI/TE), is redefined in the framework of Rényi entropy (RCMI/RTE). Using numerically generated data with a defined causal structure and examples of real data from the climate system, it is demonstrated that RCMI/RTE is able to identify the cause variable responsible for the occurrence of extreme values in an effect variable. In the presented example, the Siberian High was identified as the cause responsible for the increased probability of cold extremes in the winter and spring surface air temperature in Europe, while the North Atlantic Oscillation and blocking events can induce shifts of the whole temperature probability distribution.

Department of Complex Systems Institute of Computer Science of the Czech Academy of Sciences Pod Vodárenskou věží 2 182 00 Prague 8 Czech Republic

Institute of Measurement Science Slovak Academy of Sciences Dúbravská cesta 9 841 04 Bratislava Slovakia

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