Testing procedures for non-stationarity and non-linearity in physiological signals

Most of the physiological signals (EEG, ECG, blood flow, human gait, etc.) characterize by complex dynamics including both non-stationarities and non-linearities. These time series resemble red noise with long-range correlation and 1/(fβ) power spectrum. A question arises as to how to distinguish the characteristics of the process underlying the signal dynamics from the properties of the observed time series. The classical methods to determine possible non-linear (chaotic) dynamics (e.g. correlation dimension) often fail in such signals because of relatively short data records containing stochastic components and non-stationarities. We report an application of several approaches, aimed at (1) determining of the non-stationarities in the signals and (2) testing whether non-linear dynamics exists. Assessment of the intrinsic correlation properties of the dynamic process and distinguishing the same from external trends was performed using singular spectra and detrended fluctuation analysis. The existence of non-linear dynamics was tested by correlation dimension (modified algorithm of re-embedding) and by correlation integrals of real and surrogate data. The correlation integrals of real signal and surrogate data sets were statistically compared using Kolmogorov–Smirnov (K–S) test. The procedures were tested on EEG and laser-Doppler (LD) blood flow. Our suggestion is that no one approach taken alone is the best for our aims. Instead, a battery of methods should be used.