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BioMed Research International
Volume 2015, Article ID 140837, 8 pages
Research Article

A Time-Series Model of Phase Amplitude Cross Frequency Coupling and Comparison of Spectral Characteristics with Neural Data

The Department of Mathematics & Statistics, Boston University, 111 Cummington Mall, Boston, MA 02215, USA

Received 25 January 2015; Accepted 5 March 2015

Academic Editor: Tjeerd Boonstra

Copyright © 2015 Kyle Q. Lepage and Sujith Vijayan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 proposed models, based on multiplying a pulsatile function of a low-frequency oscillation () with an unobserved and high-frequency component, yields a process with a spectrum that is consistent with observation. Other models, 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 series model as a summation of three component weak-sense stationary (WSS) processes, namely, , , and , with a noise process. The process is constructed as a product of a latent and unobserved high-frequency process with a function of the lagged, low-frequency oscillatory component (). 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.