Causality analysis of neural connectivity: New tool and limitations of spectral Granger causality

Granger causality (GC) is one of the most popular measures to reveal causality influence of time series based on the estimated linear regression model and has been widely applied in economics and neuroscience due to its simplicity, understandability and easy implementation. Especially, its counterpart in frequency domain, spectral GC, has recently received growing attention to study causal interactions of neurophysiological data in different frequency ranges. In this paper, on the one hand, for one equality in the linear regression model (frequency domain) we point out that all items at the right-hand side of the equality make contributions (thus have causal influence) to the unique item at the left-hand side of the equality, and thus a reasonable definition for causality from one variable to another variable (i.e., the unique item) should be able to describe what percentage the variable occupies among all these contributions. Along this line, we propose a new spectral causality definition. On the other hand, we point out that spectral GC has its inherent limitations because of the use of the transfer function of the linear regression model and as a result may not reveal real causality at all and lead to misinterpretation result. By one example we demonstrate that the results of spectral GC analysis are misleading but the results from our definition are much reasonable. So, our new tool may have wide potential applications in neuroscience.