The measure of dimensional complexity has the potential for feature extraction, modeling and prediction of EEG signals. However, the nonlinear dynamics of neuronal processes is under criticism that EEG signals may have a simpler stochastic description and chaotic dynamical measures of EEG may be spurious or unnecessary. Surrogate-data testing has been propounded to detect nonlinearity and chaos in experimental time series and to differentiate it from linear stochastic processes or colored noises. The surrogate data tests of brain signals (EEG) have produced equivocal results. Therefore, we examine the surrogate testing procedure using numerical data of classical chaotic systems, mixed sine waves, white Gaussian and colored Gaussian noises and typical EEGs. White Gaussian noise and classical chaotic time series are easily discerned by the surrogate-data test. However, a colored Gaussian noise data of low correlation dimensions (D2) or mixed sine waves containing less number of sinusoids show behaviors similar to the low dimensional deterministic chaotic systems. There are significant differences in D2 values between the original and surrogate data sets. The colored Gaussian noise appears linear and stochastic only when there is an increased randomness in its pattern and the signal is high dimensional. Our results clearly indicate that the "surrogate testing" alone may not be a sufficient test for distinguishing colored noises from low dimensional chaos. The EEG time series produce finite correlation dimensions. The surrogate testing of 8 independent realizations of different forms of EEG activities produce significantly different D2 values than the original data sets. Apparently many natural phenomena follow deterministic chaos and as the dimensional complexity of the system increases (D2 > 5) it may approximate a stochastic process. Thus EEG appears unlikely to have originated from a linear system driven by white noise.
Detecting nonlinearity in time series driven by non-Gaussian noise: the case of river flows
