Evaluation of Granger causality measures for constructing networks from multivariate time series

TL;DR

This study evaluates various Granger causality measures for constructing causality networks from multivariate time series, highlighting the effectiveness of dimension reduction techniques especially in high-dimensional data.

Contribution

It provides a comprehensive comparison of time, frequency, and phase domain Granger causality measures, emphasizing the advantages of dimension reduction in high-dimensional settings.

Findings

Dimension reduction improves causality network accuracy.

Linear model-based measures outperform others in high-dimensional data.

Multivariate measures better capture complex coupling structures.

Abstract

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. These measures are in the time domain, such as model-based and information measures, the frequency domain and the phase domain. The study aims also to compare bivariate and multivariate measures, linear and nonlinear measures, as well as the use of dimension reduction in linear model-based measures and information measures. The latter is particular relevant in the study of high-dimensional time series. For the performance of the multivariate causality measures, low and high dimensional coupled dynamical systems are considered in discrete and continuous time, as well as deterministic and stochastic. The measures are evaluated and ranked according to their ability to provide causality networks that match the original coupling structure. The simulation study concludes that the Granger causality measures using dimension reduction are superior and should be preferred particularly in studies involving many observed variables, such as multi-channel electroencephalograms and financial markets.