A fatal drawback of the widely used Granger causality in neuroscience

Abstract

In 2011 [1] we proposed new causality (NC) method and demonstrated that NC method much better reveals true causality of time-invariant bivariate autoregressive model than the popular Granger causality (GC) method by several examples. In this paper, we provide more evidence that GC cannot reveal true causality, and point out the core difference between GC and NC mathematically. Given a jointly regression model in GC method one has to estimate the autoregressive model. By an illustrative example on one hand we give the exact formula for GC, which is only related to some coefficients and has nothing to do with the other coefficients, and thus GC cannot reveal true causality at all since true causality underlying the joint regression model with different time-invariant coefficients surely be different. On the other hand, we theoretically show a fatal drawback that the estimation of the autoregressive model is equivalent to taking a series of backward recursive operations, which are infeasible however for many irreversible chemical reaction models. Thus, GC method cannot be applied at all. In this case GC value by forcibly estimating the auto regressive model (i.e., taking a series of backward recursive operations) inevitably cannot reveal true causality.