Nonlinear time series analysis of human alpha rhythm
Nonlinearity is often deduced by showing that a dataset signi£cantly deviates from its phase randomized versions, i.e. surrogate data. For real data, however, non-stationarities like artifacts and onsets and offsets of rhythmic activity will cause false positives. We propose a new test which detects dynamical nonlinearity by measuring time-asymmetry, using surrogate data merely to estimate the standard deviation of the process. 
The method is applied to multi-channel MEG measurements of ongoing alpha-band activity modulated by a simple visual 
memory task involving motor activity. The signal to noise ratio was enhanced using ICA, and the analysis was performed 
on a single separated source. We found that, if the peak at 10 Hz is accompanied by a substantial higher harmonic, time 
asymmetry can be detected signifcantly in virtually any epoch of 3 second duration. Finally, we applied our recently proposed method to estimate correlation dimension for noisy data. We found very satisfactory scaling plots with dimension around 1.5. As a byproduct, we showed that the nondeterministic fraction can be explained almost completely by external noise.