Circular Correlation Methods for the Analysis of Oscillations in Dependent Time Series

Phases of signals can be regarded as circular data. Time series of phases statistically depend in time. There are also dependencies between diverse circular time series. Instead of relative-phase-methods such as phase-coherence we use a circular correlation coefficient to quantify existing dependence. Based on this coefficient we built correlation matrices. After validation in simulations, we applied the method to phase time series of electroencephalographic data. The method, developed, was positively tested and can be used for oscillation detection and to find couplings between time series considering phase information.