A Time-Series Model of Phase Amplitude Cross Frequency Coupling and Comparison of Spectral Characteristics with Neural Data
Stochastic processes that exhibit cross-frequency coupling (CFC) are introduced. The ability of these processes to model observed CFC in neural recordings is investigated by comparison with published spectra. One of the proposedmodels, based onmultiplying a pulsatile function of a low-frequency oscillation (𝜃) with an unobserved and high-frequency component, yields a process with a spectrumthat is consistent with observation. Othermodels, such as those employing a biphasic pulsatile function of a low-frequency oscillation, are demonstrated to be less suitable.We introduce the full stochastic process time seriesmodel as a summation of three component weak-sense stationary (WSS) processes, namely, 𝜃, 𝛾, and 𝜂, with 𝜂 a 1/𝑓𝛼 noise process. The 𝛾 process is constructed as a product of a latent and unobserved high-frequency process 𝑥 with a function of the lagged, low-frequency oscillatory component (𝜃). After demonstrating that the model process is WSS, an appropriate method of simulation is introduced based upon the WSS property.This work may be of interest to researchers seeking to connect inhibitory and excitatory dynamics directly to observation in a model that accounts for known temporal dependence or to researchers seeking to examine what can occur in a multiplicative time-domain CFC mechanism.