Granger Causality Inference and Time Reversal

A fundamental issue in the study of a complex system is the detection and characterization of causal dependence among components of the system. The system's components are represented by a set of selected and simultaneously recorded variables. Omitting observations of a relevant variable in a system, the Granger causality analysis can lead to false detections. Haufe et al. (2013) suggested using time reversal for testing Granger causality to alleviate the problem of spurious causality. Here we investigate the behavior of the so-called time-reversed Grange causality on different nonlinear dynamical systems with a known causal structure. As our experimental results show, the impact of a hidden influential variable cannot be excluded by using the time-reversed Granger causality. On the other hand, the time-reversed Granger causality, by the definition, can lead to false rejections in the case of a bidirectional causal connection between variables.