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Multivariate brain signals appear often as realizations of nonstationary processes that can be modeled as locally stationary time series. A very powerful approach consists in fitting time varying Vector AutoRegressive models (tvVAR), but the high number of parameters of such a model makes it very complicated to carry online estimation.
Existing methods such as the kalman filter or recursive least squares provide interesting results but they are not suitable when the parameters are smooth functions of time. Furthermore these techniques can have a prohibitive cost as the dimension of the time series increases.
We propose a new online estimation approach that provides smooth estimates over time. Our approach can be viewed as a modified maximum liklihood approach that has a Bayesian interpretation. We apply our technique to simulated tvVAR time series and show the supperiority of our approach in capturing the smooth dynamics of the parameters, filnally we apply this technique to brain signals (both LFP and EEG signals) in order to study different scientific questions.
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