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

Tom Edinburgh,Ari Ercole,Stephen J Eglen

doi:10.1063/5.0053519

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 the context of time series data. We evaluate the performance of ten prominent causality indices for bivariate time series across four simulated model systems that have different coupling schemes and characteristics. Pairwise correlations between different methods, averaged across all simulations, show that there is generally strong agreement between methods, with minimum, median, and maximum Pearson correlations between any pair (excluding two similarity indices) of 0.298, 0.719, and 0.955, respectively. In further experiments, we show that these methods are not always invariant to real-world relevant transformations (data availability, standardization and scaling, rounding errors, missing data, and noisy data). We recommend transfer entropy and nonlinear Granger causality as particularly strong approaches for estimating bivariate causal relationships in real-world applications. Both successfully identify causal relationships and a lack thereof across multiple simulations, while remaining robust to rounding errors, at least 20% missing data and small variance Gaussian noise. Finally, we provide flexible open-access Python code for computation of these methods and for the model simulations.

Highlights

No general method exists to identify causal structures within complex systems, and there is no single consistent and unifying notion of quantitative causality estimation for time series data
We reproduce the results from Ref. 18, evaluating the performance of all methods including the additional coarse-grained transinformation rate (CTIR) and convergent cross mapping (CCM), plus effective transfer entropy (ETE) using histogram binning and transfer entropy (TE) using KSG
Lungarella et al.18 note that nonlinear Granger causality1 (GC) (NLGC) is numerically unstable for “small” T and computationally expensive for “large” T, which we suggest may be partly due to their use of fuzzy cmeans

Summary

Introduction

No general method exists to identify causal structures within complex systems, and there is no single consistent and unifying notion of quantitative causality estimation for time series data. We identified and assessed a widely used subset of indices for directed bivariate causality inference, concentrating on methods involving univariate embeddings to describe the recent history of the system (Sec. II). We extend this work by proposing a set of modifications that can be made to simulated data prior to causal estimation in order to investigate sensitivity of each method to data availability, scaling, missing data, rounding, and Gaussian noise (Sec. III). Each of these reproduces phenomena that often occur in real-world data, such as when instruments have a fixed measurement precision and data are reported with rounding errors. We believe that these tests should provide in-depth benchmarking criteria for new proposed methodologies.

Methods

Results

Conclusion