  Experimentally observed networks of interacting dynamical systems are
inferred from recorded multivariate time series by evaluating a statistical
measure of dependence, usually the cross-correlation coefficient, or mutual
information. These measures reflect dependence in static probability
distributions, generated by systems' evolution, rather than coherence of
systems' dynamics. Moreover, these "static" measures of dependence can be
biased due to properties of dynamics underlying the analyzed time series.
Consequently, properties of local dynamics can be misinterpreted as properties
of connectivity or long-range interactions. We propose the mutual information
rate as a measure reflecting coherence or synchronization of dynamics of two
systems and not suffering by the bias typical for the "static" measures. We
demonstrate that a computationally accessible estimation method, derived for
Gaussian processes and adapted by using the wavelet transform, can be effective
for nonlinear, nonstationary and multiscale processes. The discussed problem
and the proposed method are illustrated using numerically generated data of
coupled dynamical systems as well as gridded reanalysis data of surface air
temperature as the source for the construction of climate networks. In
particular, scale-specific climate networks are introduced.
