Multiplicatively modulated exponential autoregressive model for corticomuscular functional coupling

An exponential autoregressive model representing the time-varying interaction between variables within the frequency domain is proposed. As opposed to earlier models, the exogenous variables are included into the autoregressive coefficients multiplicatively in order to modulate the fluctuation characteristics of the data. We have called this model the multiplicatively modulated exponential autoregressive (mmExpAR) model. In our present research, we apply the model to the study of corticomuscular functional coupling, which can be evaluated by the relationship between an electrocorticogram (ECoG) and an electromyogram (EMG) time series. In contrast with conventional time-series models, the proposed model reflects the data-generated structure of the system, with which the ECoG fluctuation modulates the EMG fluctuation. Because such a relationship is usually discussed within a physiological framework of information transfer for each individual neuron, the present modeling approach has the advantage of being able to use real data such as the summation of postsynaptic potentials and the population of action potentials of neuromuscular units.