Opposition of two informational quantifiers of directional coupling between stochastic systems

D. A. Smirnov<sup>ab

a</sup> Saratov State University
^b Saratov Branch, Kotel'nikov Institute of Radio-Engineering and Electronics, Russian Academy of Sciences

Abstract: The work studies two widely known information-theoretic tools for estimation of directional couplings (mutual influences) between observed processes – transfer entropy and Liang–Kleeman information flow. They are formally similar, have measurement units with the same name and, indeed, often characterize a coupling in a similar sense. However, it is shown here with an exemplary stochastic system within the framework of dynamical causal effects that situations, where these quantifiers behave in an opposite way (one of them increases, while another one decreases) under a change of governing parameters, are typical. Then, the two quantifiers characterize a coupling in two essentially different senses which circumstance is important and should be taken into account in their practical applications.

Keywords: stochastic dynamical systems, information-theoretic quantifiers of directional couplings, time series.

Received: 23.12.2024
Revised: 12.03.2025
Accepted: 27.03.2025

DOI: 10.61011/PJTF.2025.12.60616.20234

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