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Article

Causality in Reversed Time Series: Reversed or Conserved?

by 1,2 and 1,3,*
1
Institute of Computer Science, Czech Academy of Sciences, Pod Vodarenskou Vezi 271/2, 182 07 Prague, Czech Republic
2
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Brehova 7, 115 19 Prague, Czech Republic
3
National Institute of Mental Health, Topolova 748, 250 67 Klecany, Czech Republic
*
Author to whom correspondence should be addressed.
Academic Editors: Mohammad Reza Rahimi Tabar and Dimitris Kugiumtzis
Entropy 2021, 23(8), 1067; https://doi.org/10.3390/e23081067
Received: 19 May 2021 / Revised: 11 August 2021 / Accepted: 13 August 2021 / Published: 17 August 2021
The inference of causal relations between observable phenomena is paramount across scientific disciplines; however, the means for such enterprise without experimental manipulation are limited. A commonly applied principle is that of the cause preceding and predicting the effect, taking into account other circumstances. Intuitively, when the temporal order of events is reverted, one would expect the cause and effect to apparently switch roles. This was previously demonstrated in bivariate linear systems and used in design of improved causal inference scores, while such behaviour in linear systems has been put in contrast with nonlinear chaotic systems where the inferred causal direction appears unchanged under time reversal. The presented work explores the conditions under which the causal reversal happens—either perfectly, approximately, or not at all—using theoretical analysis, low-dimensional examples, and network simulations, focusing on the simplified yet illustrative linear vector autoregressive process of order one. We start with a theoretical analysis that demonstrates that a perfect coupling reversal under time reversal occurs only under very specific conditions, followed up by constructing low-dimensional examples where indeed the dominant causal direction is even conserved rather than reversed. Finally, simulations of random as well as realistically motivated network coupling patterns from brain and climate show that level of coupling reversal and conservation can be well predicted by asymmetry and anormality indices introduced based on the theoretical analysis of the problem. The consequences for causal inference are discussed. View Full-Text
Keywords: causality; time reversal; temporal symmetry; reversed time series; vector autoregressive process; random networks; brain network; climate network causality; time reversal; temporal symmetry; reversed time series; vector autoregressive process; random networks; brain network; climate network
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MDPI and ACS Style

Kořenek, J.; Hlinka, J. Causality in Reversed Time Series: Reversed or Conserved? Entropy 2021, 23, 1067. https://doi.org/10.3390/e23081067

AMA Style

Kořenek J, Hlinka J. Causality in Reversed Time Series: Reversed or Conserved? Entropy. 2021; 23(8):1067. https://doi.org/10.3390/e23081067

Chicago/Turabian Style

Kořenek, Jakub, and Jaroslav Hlinka. 2021. "Causality in Reversed Time Series: Reversed or Conserved?" Entropy 23, no. 8: 1067. https://doi.org/10.3390/e23081067

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