Institute of Computer Science, Academy of Sciences of the Czech Republic
Pod vodárenskou vezí 2, 182 07 Prague 8, Czech Republic
Krakovska A., Jakubik J., Chvostekova M.
Institute of Measurement Science, Slovak Academy of Sciences, Dubravska cesta 9, 841 04 Bratislava, Slovak Republic
Using several methods for detection of causality in time series we show in a numerical study that coupled chaotic dynamical systems violate the first principle of Granger causality that the cause precedes the effect. Reminding the relation between entropy production and temporal irreversibility of chaotic processes we argue that such a violation cannot occur in nature, just in formal applications of time series analysis methods. The obtained knowledge, however, can help to understand the type of causal relations observed in experimental data, namely can help to distinguish linear transfer of time-delayed signals from nonlinear interactions. We illustrate these findings in causality detected in experimental time series from the climate system and mammalian cardio-respiratory interactions.