Inferring directed spectral information flow between mixed-frequency time series.

Identifying directed spectral information flow between multivariate time series is important for many applications in finance, climate, geophysics and neuroscience. Spectral Granger causality (SGC) is a prediction-based measure characterizing directed information flow at specific oscillatory frequencies. However, traditional vector autoregressive (VAR) approaches are insufficient to assess SGC when time series have mixed frequencies (MF) or are coupled by nonlinearity. Here we propose a time-frequency canonical correlation analysis approach ("MF-TFCCA") to assess the strength and driving frequency of spectral information flow. We validate the approach with intensive computer simulations on MF time series under various interaction conditions and assess statistical significance of the estimate with surrogate data. We further apply MF-TFCCA to real-life finance, climate and neuroscience data. Our analysis framework provides an exploratory and computationally efficient approach to quantify directed information flow between MF time series in the presence of complex and nonlinear interactions.