Time series analysis of trial-to-trial variability of MEG power spectrum during rest state, unattented listening and frequency-modulated tones classification

The nonstationarity of EEG/MEG signals is important for understanding the functioning of human brain. From the previous research we know that even very short, i.e. 250--500ms MEG signals are variance-nonstationary. The covariance of stochastic process is mathematically associated with its spectral density, therefore we investigate how the spectrum of such nonstationary signals varies in time. We analyze the data from 148-channel MEG, that represent rest state, unattented listening and frequency-modulated tones classification. We transform short-time MEG signals to the frequency domain using the FFT algorithm and for the dominant frequencies 8--12 Hz we prepare the time series representing their trial-to-trial variability. Then, we test them for level- and trend-stationarity, unit root, heteroscedasticity and gaussianity and based on their properties we propose the ARMA-modelling for their description. The analyzed time series have the weakly stationary properties independently of the functional state of brain and localization. Only their small percentage, mostly related to the cognitive task, still presents nonstationarity. The obtained mathematical models show that the spectral density of analyzed signals depends on only 2--3 previous trials. The presented method has limitations related to FFT resolution and univariate models, but it is not computationally complicated and allows to obtain a low-complex stochastic models of the EEG/MEG spectrum variability. Although the physiological short-time MEG signals are in principle nonstationary in time domain, its power spectrum at the dominant frequencies varies as weakly stationary stochastic process. Described technique has the possible applications in prediction of the EEG/MEG spectral properties in theoretical and clinical neuroscience.