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This study presents a least mean squares (LMS) algorithm for the ensemble modeling of a multivariate ARMA process. Generally, an LMS algorithm makes possible the tracking of parameters for nonstationary time series. Our estimation incorporates multiple process observations that improve the accuracy of the parameter estimation. As a consequence, the estimation sequences come close to the true model parameters with a fast adaptation speed. This advantage also holds true of spectral quantities (e.g., the momentary coherence), which are derived from the model parameters. Thus the extension of the ARMA fitting from one to multiple trajectories allows the investigation of nonstationary biological signals with an increased time resolution. The applicability of the algorithm is demonstrated for event-related EEG coherence analysis of the Sternberg task. The changing interaction between posterior association cortex and anterior brain area was shown for verbal and nonverbal stimuli by means of the time-variant theta coherence.

Neuronal activity during information processing and muscle activity are generally characterized by oscillations. Mostly, widespread areas are involved and electrophysiological signals are measured on different sites of the cortex or of the muscle.In order to investigate functional relationships between different components of multidimensional electrophysiological signals, coherence and phase analyses turned out to be useful tools. These parameters allow the investigation of synchronization phenomena with regard to oscillations of defined frequencies or frequency bands.Coherence and phase are closely connected spectral parameters. Coherence may be understood as a measure of phase stability. Whereas coherence describes the amount of common information with regard to oscillations within certain frequency bands, the corresponding phase, from which time delays of these oscillations can be computed, hints at the direction of information transfer through oscillation.Coherence and phase analysis of surface EMG during continuous activity of deep and superficial muscles show distinct differences due to volume conduction properties of myoelectrical signals. Superficial activity therefore is characterized by significant coherence and stable phase relationships, which, additionally, can be used to determine motor unit action potential (MUAP) propagation velocity along the fibre direction without application of invasive methods. Deep muscle activity lacks significant coherence.Mental processes can be very brief and cooperation between different areas may be highly dynamic. For this reason in addition to usual Fourier estimation of coherence and phase, a two-dimensional approach of adaptive filtering was developed to estimate coherence and phase continuously in time. Statistical and dynamic properties of instantaneous phase are discussed.In order to demonstrate the value of this method for studying higher cognitive processes the method was applied to EEG recorded during word processing. During visual presentation of abstract nouns an information transfer through the propagation of oscillations from visual areas to frontal association areas in the α 1 -frequency band could be verified within the first 400 ms. In contrast, in case of auditory presentation positive phases from the temporal electrode locations T3 and T4 towards the occipital areas appear within the time interval of 300 ms-600 ms. The α 1 -band predominately seems to reflect sensory processing and attention processes.

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Commonly, coherence and correlation are used to describe interrelations between EEG signals. But, on this basis, the investigation of causality or direction of interrelations is not possible. The general idea of causality between two signals may be expressed in terms of upgrading the predictability of one signal bye the knowledge of the past of the other signal. The best established approach in this context is the so-called Granger causality. The study present an adaptive estimation of Granger causality, which allows to detect dynamic causal relations within time intervals of less 100 ms. The time-variant Granger causality is applied to EEG data of the Stroop task. It could be shown, that conflict situation generates a dense web of directed interactions from posterior to anterior cortical areas.