On the complementarity of ordinal patterns-based entropy and time asymmetry metrics

Entropy and time asymmetry are two intertwined aspects of a system's dynamics, with the production of entropy marking a clear direction in the temporal dimension. In the last few years, metrics to quantify both properties in time series have been designed around the same concept, i.e., the use of ordinal patterns. In spite of this, the relationship between these two families of metrics is yet not well understood. In this contribution, we study this problem by constructing an entropy-time asymmetry plane and evaluating it on a large set of synthetic and real-world time series. We show how the two metrics can at times behave independently, the main reason being the presence of patterns with turning points; due to this, they yield complementary information about the underlying systems, and they have different discriminating performance.

Automated summary

Entropy and time asymmetry are intertwined aspects of a system's dynamics, and metrics based on ordinal patterns have been designed to quantify both properties in time series. However, the relationship between these metrics is not well understood. In this study, an entropy-time asymmetry plane is constructed and evaluated on synthetic and real-world time series, revealing that the two metrics can behave independently due to the presence of turning point patterns.