Directional coupling detection through cross-distance vectors

TL;DR

This paper introduces a new, robust, and model-free causality measure based on cross-distance vectors for detecting directional coupling in complex systems, effective even with noise and short data segments.

Contribution

It presents a novel state space causality measure that improves accuracy in coupling detection and includes an optimal parameter selection procedure, applicable to real-world data.

Findings

The method accurately detects coupling direction in various dynamical systems.

It is robust to noise and artefacts in data.

The approach effectively analyzes short time series and real physiological data.

Abstract

Inferring the coupling direction from measured time series of complex systems is challenging. We propose a new state space based causality measure obtained from cross-distance vectors for quantifying interaction strength. It is a model-free noise-robust approach that requires only a few parameters. The approach is applicable to bivariate time series and is resilient to artefacts and missing values. The result is two coupling indices that quantify coupling strength in each direction more accurately than the already established state space measures. We test the proposed method on different dynamical systems and analyse numerical stability. As a result, a procedure for optimal parameter selection is proposed, circumventing the challenge of determining the optimal embedding parameters. We show it is robust to noise and reliable in shorter time series. Moreover, we show that it can detect cardiorespiratory interaction in measured data. A numerically efficient implementation is available at https://repo.ijs.si/mbresar/cd-vec.