Estimating Granger causality from Fourier and wavelet transforms of time series data

Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data. Here, we extend the framework of nonparametric 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.

💡 Research Summary

The paper introduces a non‑parametric framework for estimating Granger‑causality spectra directly from Fourier and wavelet transforms of time‑series data. Traditional Granger causality analysis relies on vector autoregressive (VAR) models, which require careful model order selection, assume stationarity, and can fail when the underlying dynamics are nonlinear or non‑stationary. By contrast, the authors propose to compute the causality spectrum without fitting any parametric model.

The method proceeds as follows. For two scalar time series (x(t)) and (y(t)), the discrete Fourier transform yields complex spectra (X(f)) and (Y(f)). From these, the auto‑spectra (S_{xx}(f)=E