Linked by dynamics: wavelet--based mutual information rate as a connectivity measure and scale-specific networks

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.