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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 21, issue 5
Nonlin. Processes Geophys., 21, 929–937, 2014
https://doi.org/10.5194/npg-21-929-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Complex network approaches to analyzing and modeling nonlinear...

Nonlin. Processes Geophys., 21, 929–937, 2014
https://doi.org/10.5194/npg-21-929-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 11 Sep 2014

Research article | 11 Sep 2014

Estimating time delays for constructing dynamical networks

E. A. Martin and J. Davidsen E. A. Martin and J. Davidsen
  • Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, T2N 1N4, Canada

Abstract. Dynamical networks – networks inferred from multivariate time series – have been widely applied to climate data and beyond, resulting in new insights into the underlying dynamics. However, these inferred networks can suffer from biases that need to be accounted for to properly interpret the results. Here, we report on a previously unrecognized bias in the estimate of time delays between nodes in dynamical networks inferred from cross-correlations, a method often used. This bias results in the maximum correlation occurring disproportionately often at large time lags. This is of particular concern in dynamical networks where the large number of possible links necessitates finding the correct time lag in an automated way. We show that this bias can arise due to the similarity of the estimator to a random walk, and are able to map them to each other explicitly for some cases. For the random walk there is an analytical solution for the bias that is closely related to the famous Lévy arcsine distribution, which provides an upper bound in many other cases. Finally, we show that estimating the cross-correlation in frequency space effectively eliminates this bias. Reanalysing large lag links (from a climate network) with this method results in a distribution peaked near zero instead, as well as additional peaks at the originally assigned lag. Links that are reassigned smaller time lags tend to have a smaller distance between them, which indicates that the new time delays are physically reasonable.

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