Relevance of surrogate-data testing in electroencephalogram analysis

Surrogate-data testing has been propounded to detect nonlinearity and chaos in experimental time series and to differentiate them from linear stochastic processes or colored noises. The surrogate tests of brain signals [electroencephalograms (EEG’s)] 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 EEG’s. The white Gaussian noise and chaotic time series are easily discerned by the surrogate-data test. However, the surrogate-data test fails to detect colored Gaussian noise data of low correlation dimensions (${\mathit{D}}_2$) or mixed sine waves containing a smaller number of wave forms. The colored Gaussian noise appears linear and stochastic only when there is an increased randomness in its pattern and the data set is high dimensional. Therefore, the ‘‘surrogate test’’ may not be a sufficient test for chaoticity and wrong conclusions can be arrived at if analyses are based only on the surrogate test. The EEG time series produce finite correlation dimensions. The surrogate testing of eight independent realizations of different forms of EEG activities produces significantly different ${\mathit{D}}_2$ values (Student’s t test) than the original data sets. Thus the EEG is proven to be chaotic in nature. Apparently many natural phenomena follow deterministic chaos, and as the dimensional complexity of the system increases (${\mathit{D}}_2$>5) it may be approximated to be stochastic. © 1996 The American Physical Society.