Reliability of the Granger causality inference

Douglas Zhou, Yaoyu Zhang, Yanyang Xiao, David Cai

Research output: Contribution to journalArticlepeer-review


How to characterize information flows in physical, biological, and social systems remains a major theoretical challenge. Granger causality (GC) analysis has been widely used to investigate information flow through causal interactions. We address one of the central questions in GC analysis, that is, the reliability of the GC evaluation and its implications for the causal structures extracted by this analysis. Our work reveals that the manner in which a continuous dynamical process is projected or coarse-grained to a discrete process has a profound impact on the reliability of the GC inference, and different sampling may potentially yield completely opposite inferences. This inference hazard is present for both linear and nonlinear processes. We emphasize that there is a hazard of reaching incorrect conclusions about network topologies, even including statistical (such as small-world or scale-free) properties of the networks, when GC analysis is blindly applied to infer the network topology. We demonstrate this using a small-world network for which a drastic loss of small-world attributes occurs in the reconstructed network using the standard GC approach. We further show how to resolve the paradox that the GC analysis seemingly becomes less reliable when more information is incorporated using finer and finer sampling. Finally, we present strategies to overcome these inference artifacts in order to obtain a reliable GC result.

Original languageEnglish (US)
Article number043016
JournalNew Journal of Physics
StatePublished - Apr 2014


  • Causal information flow
  • Reliability of causal inference
  • Sampling hazards
  • Small-world topology

ASJC Scopus subject areas

  • General Physics and Astronomy


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