Generalized state - space models for modeling nonstationary EEG time - series

Contemporary neuroscientific research has access to various techniques for recording time-resolved data relating to human brain activity: electroencephalography (EEG) and magnetoencephalography (MEG) record the electromagnetic fields generated by the brain, while other techniques, such as near-infrared spectroscopy (NIRS) and functional magnetic resonance imaging (fMRI) are sensitive to the local metabolic activity of brain tissue. Time-resolved data contain valuable information on the dynamical processes taking place in brain. EEG and MEG time-series are especially promising, since the electromagnetic fields of the brain are directly reflecting the activation of neural populations; furthermore these time-series can be recorded with high temporal resolution. Extraction of the dynamic changes captured by EEG/MEG recordings is an ideal application for time-series analysis [10]. From the multiplicity of concepts and methods for time-series analysis that have been applied to neuroscientific time-series, we focus here on predictive modeling, i.e., finding a predictor for future time-series values, based on present and past values. More precisely, we will discuss a particular class of predictive modeling that is attracting considerable attention due to its wide applicability: the state-space model [2, 3, 6, 12, 13]. Because nonstationary phenomena—such as sudden phase transitions relating to qualitative changes in dynamical behavior—cannot be modeled well using standard