Information-based estimation of causality networks from high-dimensional multivariate time series

One of the most challenging aspects in the study of the complex dynamical systems is the estimation of their underlying, interdependence structure. Being in the era of Big Data, this problem gets even more complicated since more observed variables are available. To estimate direct causality effects in this setting, dimension reduction has to be employed in the Granger causality measure. The measure should also be capable to detect non-linear effects, persistently present in real-world complex systems. The model-free information-based measure of partial mutual information from mixed embedding (PMIME) has been developed to address these issues and it was found to perform well on multivariate time series of moderately high dimension. Here, the problem of forming complex networks from direct, possibly non-linear, high-dimensional time series at the order of hundreds is investigated. The performance of the measure PMIME is tested on two coupled dynamical systems in discrete time (coupled Hénon maps) and continuous time (coupled Mackey–Glass delay differential equations). It is concluded that the correct detection of the underlying causality network depends mainly on the network density rather than on its size (number of nodes). Finally, the effect of network size is investigated in the study of the British stock market in the period around Brexit.