Causality and information transfer in systems with extreme events

The mathematical formulation of causality in measurable terms of predictability was given by the father of cybernetics N. Wiener [1] and formulated for time series by C.W.J. Granger [2]. The Granger causality is based on the evaluation of predictability in bivariate autoregressive models. This concept has been generalized for nonlinear systems using methods rooted in information theory [3,4]. The information-theoretic approach, defining causality as information transfer, has been successful in many applications and generalized to multivariate data and causal networks [e.g., 5]. This approach, rooted in the information theory of Shannon, usually ignores two important properties of complex systems, such as the Earth climate: the systems evolve on multiple time scales and their variables have heavy-tailed probability distributions. While the multiscale character of complex dynamics, such as air temperature variability, can be studied within the Shannonian framework [6, 7], the entropy concepts of Rényi and Tsallis have been proposed to cope with variables with heavy-tailed probability distributions. We will discuss how such non-Shannonian entropy concepts can be applied in inference of causality in systems with heavy-tailed probability distributions and extreme events, using examples from the climate system.

This study was supported by the Czech Science Foundation, project GA19-16066S.

 

 [1] N. Wiener, in: E. F. Beckenbach (Editor), Modern Mathematics for Engineers (McGraw-Hill, New York, 1956)

[2] C.W.J. Granger, Econometrica 37 (1969) 424

[3] K. Hlaváčková-Schindler et al., Phys. Rep. 441 (2007)  1

[4] M. Paluš, M. Vejmelka, Phys. Rev. E 75 (2007) 056211

[5] J. Runge et al., Nature Communications 6 (2015) 8502

[6] M. Paluš, Phys. Rev. Lett. 112 (2014) 078702

 [7] N. Jajcay, J. Hlinka, S. Kravtsov, A. A. Tsonis, M. Paluš, Geophys. Res. Lett. 43(2) (2016) 902–909