  The goal of this paper is to develop a measure for characterizing complex
dependence between stationary time series that cannot be captured by
traditional measures such as correlation and coherence. Our approach is to use
copula models of functionals of the Fourier coefficients which is a
generalization of coherence. Here, we use standard parametric copula models
with a single parameter both from elliptical and Archimedean families. Our
approach is to analyze changes in local field potentials in the rat cortex
prior to and immediately following the onset of stroke. We present the
necessary theoretical background, the multivariate models and an illustration
of our methodology on these local field potential data. Simulations with
non-linear dependent data show information that were missed by not taking into
account dependence on specific frequencies. Moreover, these simulations
demonstrate how our proposed method captures more complex non-linear dependence
between time series. Finally, we illustrate our copula-based approach in the
analysis of local field potentials of rats.
