Abstract
Measures of the direction and strength of the interdependence among time series from multivariate systems are evaluated based on their statistical significance and discrimination ability. The best-known measures estimating direct causal effects, both linear and nonlinear, are considered, i.e., conditional Granger causality index (CGCI), partial Granger causality index (PGCI), partial directed coherence (PDC), partial transfer entropy (PTE), partial symbolic transfer entropy (PSTE) and partial mutual information on mixed embedding (PMIME). The performance of the multivariate coupling measures is assessed on stochastic and chaotic simulated uncoupled and coupled dynamical systems for different settings of embedding dimension and time series length. The CGCI, PGCI and PDC seem to outperform the other causality measures in the case of the linearly coupled systems, while the PGCI is the most effective one when latent and exogenous variables are present. The PMIME outweighs all others in the case of nonlinear simulation systems.
Highlights
The quantification of the causal effects among simultaneously observed systems from the analysis of time series recordings is essential in many scientific fields, ranging from economics to neurophysiology.Estimating the inter-dependence among the observed variables provides valuable knowledge about the processes that generate the time series
The partial directed coherence (PDC) is estimated for the range of frequencies, [0, 0.4], since the auto-spectra of all the variables are higher in the range, [0, 0.2], while variable, X3, exhibits a peak in the range, [0.2, 0.4]
The specificity of the partial mutual information on mixed embedding (PMIME) is improved by the increase of n, and the percentage of positive PMIME values in case of no direct causal effects varies from 0% to 22% for n = 512, while for n = 2048, it varies from 0% to 1%
Summary
The quantification of the causal effects among simultaneously observed systems from the analysis of time series recordings is essential in many scientific fields, ranging from economics to neurophysiology. Most of the non-causality tests, built on the Granger causality concept and applied in economics, are based on the modeling of the multivariate time series. Techniques accounting for the effect of the confounding variables have been introduced, termed direct causality measures, which are more appropriate when dealing with multivariate time series [15,16,17]. We compare model-based methods, both in the time and frequency domain, and information theoretic multivariate causality measures that are able to distinguish between direct and indirect causal effects. We include in the study most of the known direct causality measures of these classes, i.e., CGCI and PGCI (linear in time domain), PDC (linear in frequency domain), PTE, PSTE and PMIME (from information theory).
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