Testing different methodologies for Granger causality estimation: A simulation study

Granger causality (GC) is a method for determining whether and how two time series exert causal influences one over the other. As it is easy to implement through vector autoregressive (VAR) models and can be generalized to the multivariate case, GC has spread in many different areas of research such as neuroscience and network physiology. In its basic formulation, the computation of GC involves two different regressions, taking respectively into account the whole past history of the investigated multivariate time series (full model) and the past of all time series except the putatively causal time series (restricted model). However, the restricted model cannot be represented through a finite order VAR process and, when few data samples are available or the number of time series is very high, the estimation of GC exhibits a strong reduction in accuracy. To mitigate these problems, improved estimation strategies have been recently implemented, including state space (SS) models and partial conditioning (PC) approaches. In this work, we propose a new method to compute GC which combines SS and PC and tests it together with other four commonly used estimation approaches. In simulated networks of linearly interacting time series, we show the possibility to reconstruct the network structure even in challenging conditions of data samples available.