Abstract: Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based non-parametric methods are used widely to study the spectral characteristics of these time series data. Here, we extend the framework of non-parametric spectral methods to include the estimation of Granger causality spectra for assessing directional influences. We illustrate the utility of the proposed methods using synthetic data from network models consisting of interacting dynamical systems.