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

Luca Faes1,*, Giandomenico Nollo1, and Alberto Porta2

  • 1Department of Physics and BIOtech, University of Trento, Trento, Italy
  • 2Galeazzi Orthopaedic Institute, Department of Technologies for Health, University of Milan, Milan, Italy

  • *Author to whom correspondence should be addressed: luca.faes@unitn.it
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Phys. Rev. E 83, 051112 – Published 11 May, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.051112

Abstract

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.

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      Outline

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      Phys. Rev. E 83, 051112– Published 11 May, 2011
      • Received 17 September 2010

      ©2011 American Physical Society

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