Causality indices for bivariate time series data: a comparative review of performance

TL;DR

This paper compares ten causality indices for bivariate time series, evaluating their performance across simulated models and real-world transformations, recommending transfer entropy and nonlinear Granger causality for robustness.

Contribution

It provides a comprehensive performance comparison of causality indices and offers open-source Python tools for their computation and simulation.

Findings

Transfer entropy and nonlinear Granger causality are most robust.

Causality indices vary in invariance to data transformations.

Open-access Python code is provided for practical use.

Abstract

Inferring nonlinear and asymmetric causal relationships between multivariate longitudinal data is a challenging task with wide-ranging application areas including clinical medicine, mathematical biology, economics and environmental research. A number of methods for inferring causal relationships within complex dynamic and stochastic systems have been proposed but there is not a unified consistent definition of causality in this context. We evaluate the performance of ten prominent bivariate causality indices for time series data, across four simulated model systems that have different coupling schemes and characteristics. In further experiments, we show that these methods may not always be invariant to real-world relevant transformations (data availability, standardisation and scaling, rounding error, missing data and noisy data). We recommend transfer entropy and nonlinear Granger causality as likely to be particularly robust indices for estimating bivariate causal relationships in real-world applications. Finally, we provide flexible open-access Python code for computation of these methods and for the model simulations.