Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique

Luca Faes, Giandomenico Nollo, Alberto Porta

Research output: Contribution to journalArticlepeer-review


We present an approach, framed in information theory, to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system. The approach follows a sequential procedure for nonuniform embedding of multivariate time series, whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states. A corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure. The causal coupling is detected according to the Granger notion of predictability improvement, and is quantified in terms of information transfer. We apply the approach to simulations of deterministic and stochastic systems, showing its superiority over standard uniform embedding. Effects of quantization, data length, and noise contamination are investigated. As practical applications, we consider the assessment of cardiovascular regulatory mechanisms from the analysis of heart period, arterial pressure, and respiration time series, and the investigation of the information flow across brain areas from multichannel scalp electroencephalographic recordings.

Original languageEnglish
Article number051112
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
Publication statusPublished - May 11 2011

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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