  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.
