Fitting of one ARMA model to multiple trials increases the time resolution of instantaneous coherence

Abstract

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.

Time-varying MVAR algorithms for directed connectivity analysis: Critical comparison in simulations and benchmark EEG data

“…The adaptation coefficients are used in recursive algorithms to regulate the adaptation speed of parameters estimation and have to be selected between zero and one [ 17 , 18 ]. Values close to one lead to a faster adaptation (‘adaptivity’) but also a greater variance of parameter estimates, and this trade-off holds vice versa for values close to zero [ 37 , 38 ]. Thus, if the adaptation coefficients are not properly tuned, the performance of the recursive algorithm may be significantly degraded.…”

“…When multi-trial time series are available, information from single trials can be combined in tvMVAR models to improve estimation accuracy and reliability of connectivity estimates [ 38 ]. Two strategies can be adopted to make use of multiple realizations: i) single-trial tvMVAR modeling followed by averaging across trials [ 40 , 41 ]; ii) multi-trial modeling, in which one tvMVAR model is simultaneously fitted to all trials [ 17 , 18 , 38 ]. The relative advantages of each approach and their sensitivities to parameter settings have not been systematically tested, but are important to understand when using these techniques in real data.…”

Quantitative measures of cortical functional connectivity: A state-of-the-art brief survey

“…As long as nonstationary processes in neurophysiology rapidly vary with time (tens of milliseconds), the best way of obtaining robust estimators of the functional connections would be to make a single VAR model for the entire set of function ally homogeneous EEG segments simultaneously [42].…”

“…The experimental studies in recent years show that the measures of frequency specific directed influence based on the VAR model are a prospective tool for the analysis of EEG, MEG [16,17,34,[39][40][41][42][43][44], and fMRI data [45,46]. The underlying principle of the VAR model, the rank of this method among other methods, and the practical aspects of its application are discussed in several reviews [18,34,47].…”

Extraction and recognition of electroencephalogram dynamic patterns for brain-computer interfaces

“…Temporal analysis implies tracking changes of any EEG characteristic in time; frequency analysis is related to the representation of EEG signal in the frequency domain; spatial analysis involves various processing methods for comparing the EGG characteristics in various channels of electroencephalograph. The methods of EEG spectral analysis are developed in [14][15][16], the methods of wavelet analysis in [17,18], EEG correlation analysis (analysis of autocorrelation and cross-correlation functions, linear autoregressive models, ARMA-models with time-varying coefficients, spectralcorrelation methods) are represented in [19][20][21], coherent analysis, analysis of spatial distributions of potentials, segmentation analysis, bispectral and bicoherent analysis are represented in [22][23][24][25].…”