Time-Reversibility, Causality and Compression-Complexity

Publication Type:

Journal Articles


Entropy., Volume 23 , Issue 3 , p.327 (2021)




time-reversibility; time-irreversibility; temporal asymmetry; compression-complexity; effort-to-compress; compressive potential; interventional causality; heart period variability asymmetry; sunspot numbers


Detection of the temporal reversibility of a given process is an interesting time series analysis scheme that enables the useful characterisation of processes and offers an insight into the underlying processes generating the time series. Reversibility detection measures have been widely employed in the study of ecological, epidemiological and physiological time series. Further, the time reversal of given data provides a promising tool for analysis of causality measures as well as studying the causal properties of processes. In this work, the recently proposed&nbsp;Compression-Complexity Causality (CCC)&nbsp;measure (by the authors) is shown to be free of the assumption that the "cause precedes the effect", making it a promising tool for causal analysis of reversible processes. CCC is a data-driven interventional measure of causality (second rung on the&nbsp;Ladder of Causation) that is based on&nbsp;Effort-to-Compress (ETC), a well-established robust method to characterize the complexity of time series for analysis and classification. For the detection of the temporal reversibility of processes, we propose a novel measure called the&nbsp;Compressive Potential based Asymmetry Measure. This asymmetry measure compares the probability of the occurrence of patterns at different scales between the forward-time and time-reversed process using ETC. We test the performance of the measure on a number of simulated processes and demonstrate its effectiveness in determining the asymmetry of real-world time series of sunspot numbers, digits of the transcedental number&nbsp;<inline-formula><nobr aria-hidden="true">π</nobr><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics></semantics></math></inli... heart interbeat interval variability