The goal of this paper is to develop a measure for characterizing complex dependence between 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 from both elliptical and Archimedean families. Our approach is to analyze changes in activity 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 nonlinear dependent data reveal that there is information that is missed by not taking into account dependence on specific frequencies. Moreover, these simulations demonstrate how our proposed method captures more complex nonlinear dependence between time series. Finally, we illustrate our copula-based approach in the analysis of local field potentials of rats.