Paluš Milan, Krakovská Anna, Jakubík Jozef, Chvosteková Martina
Institute of Computer Science, Czech Academy of Sciences, Pod Vodárenskou věží 2, Praha 8 182 07, Czech Republic.
Institute of Measurement Science, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava 841 04, Slovak Republic.
Chaos. 2018 Jul;28(7):075307. doi: 10.1063/1.5019944.
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. While such a violation can be observed in formal applications of time series analysis methods, it cannot occur in nature, due to the relation between entropy production and temporal irreversibility. The obtained knowledge, however, can help to understand the type of causal relations observed in experimental data, namely, it 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.
通过使用几种时间序列因果关系检测方法，我们在一项数值研究中表明，耦合混沌动力系统违反了格兰杰因果关系的首要原则，即原因先于结果。虽然在时间序列分析方法的正式应用中可以观察到这种违反情况，但由于熵产生与时间不可逆性之间的关系，它在自然界中不可能发生。然而，所获得的知识有助于理解实验数据中观察到的因果关系类型，即有助于区分延迟信号的线性传递与非线性相互作用。我们在气候系统和哺乳动物心肺相互作用的实验时间序列中检测到的因果关系中说明了这些发现。
