Parametric modeling of brain signals

In this paper, modeling of EEG signals using parametric modeling - both linear and nonlinear has been explored. Linear models include autoregressive (AR) and autoregressive moving average (ARMA) models whereas the nonlinear models considered include polynomial autoregressive (PAR) and bilinear (BL) models. Model orders for all the four models have been determined by Akaike Information Criteria. Residual variance for all the four models have been computed and used as a criterion for comparison. It is observed that the bilinear model has worked effectively than the other three models. It has been observed that the BL model has the ability to model a large class of nonlinear systems. The evidence provided in this study suggests that modeling of EEG signals is yet another useful application of the bilinear model. However in situations where computational complexity (and hence the computation time) is very important, PAR model seems to be better, though with somewhat lesser performance. One of the important observations of the study is that the nonlinear models work very well on EEG signals. It is seen that the BL model outperforms PAR. A possible reason is that EEG is a random sum of the firings of billions of neurons, which is essentially a noise input. So as BL considers the past of the noise input along with past signal values, it performs better. These results seem to imply that the systems controlling brain dynamics are nonlinear. The suitability of BL and PAR models suggest that future studies on brain dynamics should focus on nonlinear methods of analysis.