Oscillating systems with cointegrated phase processes (Q2408050)

A discrete time series is ``integrated of order 1'' if the differences between successive values is a stationary series. If a linear combination of several such time series is integrated of order zero (i.e., that combination is stationary), then the collection is said to be cointegrated. Phase synchronisation between oscillators is closely related to the idea that their phases are cointegrated. In this paper the authors present a class of coupled stochastic oscillators with linear coupling in the phases, and then present a cointegration theory for this class. They then perform and analyse simulations of three stochastic Winfree oscillators coupled in various configurations and show that co-integration analysis can recover the directionality and strength of coupling between these oscillators. They then analyse some EEG data in the same way.