Mutual information in the frequency domain

Coefficients of mutual information (MI) can provide powerful extensions of classical coefficients of correlation. In particular, they have the property of vanishing if and only if the components involved are statistically independent of each other. This characteristic can prove useful in preparatory work to model building. In this article a frequency domain variant of MI is developed and studied for bivariate stationary time series. As a scientific example an ambient seismic noise data set is studied and a lack of independence of the components inferred. The character of the dependence of the MI on frequency may be used to suggest the nature of the statistical dependence.