Validity of Time Reversal for Testing Granger Causality

Irene Winkler, Danny Panknin, Daniel Bartz, Klaus Robert Muller, Stefan Haufe

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)


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 (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 between two variables, 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.

Original languageEnglish
Article number7412766
Pages (from-to)2746-2760
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number11
Publication statusPublished - 2016 Jun 1


  • Granger causality
  • TRGC
  • noise
  • time reversal

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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