Validity of time reversal for testing Granger causality

TL;DR

This paper proves that time-reversal methods for testing Granger causality are valid for linear autoregressive processes with true interactions and are more noise-robust than traditional measures.

Contribution

It provides a theoretical proof of the validity of time-reversal Granger causality for linear processes with true interactions and demonstrates its robustness through simulations.

Findings

TRGC correctly estimates information flow and directionality in linear processes.

TRGC has similar statistical power to net Granger causality.

TRGC is more robust to measurement noise than traditional methods.

Abstract

Inferring causal interactions from observed data is a challenging problem, especially in the presence of measurement noise. To alleviate the problem of spurious causality, Haufe et al. (2013) proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time-reversed data. They show that this procedure, time-reversed Granger causality (TRGC), robustly rejects causal interpretations on mixtures of independent signals. While promising results have been achieved in simulations, it was so far unknown whether time reversal leads to valid measures of information flow in the presence of true interaction. Here we prove that, for linear finite-order autoregressive processes with unidirectional information flow, the application of time reversal for testing Granger causality indeed leads to correct estimates of information flow and its directionality. Using simulations, we further show that TRGC is able to infer correct directionality with similar statistical power as the net Granger causality between two variables, while being much more robust to the presence of measurement noise.