Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 64, Issue 11, Pages 2746-2760Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2016.2531628
Keywords
Granger causality; time reversal; noise; TRGC
Categories
Funding
- Marie Curie International Outgoing Fellowship within 7th European Community Framework Program [625991]
- BMBF project ALICE II
- Autonomous Learning in Complex Environments [01IB15001B]
- Brain Korea 21 Plus Programas
- SGER through National Research Foundation of Korea - Ministry of Education [2014055911]
- Korea Institute of Marine Science & Technology Promotion (KIMST) [2014055911] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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 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.
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