Instantaneous multivariate EEG coherence analysis by means of adaptive high-dimensional autoregressive models

This study presents an efficient algorithm for the fitting of multivariate autoregressive models (MVAR) with time-dependent parameters to multidimensional signals. Thereby, the dimension of the model may be chosen to equal the number of signal channels. The autoregressive (AR) parameter matrices are estimated by an extension of the recursive least squares (RLS) algorithm with forgetting factor. The estimation procedure includes a single trial as well as an ensemble mean approach. The latter approach allows the simultaneous fit of one mean MVAR model to a set of single trials, each of them representing the measurement of the same task. A particular advantage of this ensemble mean approach is that it requires only a low computation effort in comparison to well known procedures applied to single trials. Furthermore, the ensemble mean approach is linked with a high adaptation capability. The properties of the estimator are investigated using simulated time series. It can be demonstrated that the adaptation capability of the estimation (measured by its adaptation speed and variance) does not depend on the model dimension. The mean MVAR fit is applied to 19-dimensional EEG data, recorded during an elementary comparison procedure. The calculation of ordinary and multiple coherence is discussed. The sensitivity of the multiple instantaneous EEG coherence will be demonstrated.