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

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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 there is generally strong agreement between methods, with minimum, median and maximumPearson 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 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 particularly strong approaches for estimating bivariate causal relationships inreal-world applications. Both successfully identify causal relationships and a lack thereof across multiple simulations, whilst remaining robust to rounding error, 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.



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Chaos: an interdisciplinary journal of nonlinear science

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American Institute of Physics
TE: Engineering and Physical Sciences Research Council (EPSRC) National Productivity Investment Fund (NPIF) EP/S515334/1, reference 2089662 and Cantab Capital Institute for Mathematics of Information (CCIMI)