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Title: Modeling dependence in multivariate time series. Abstract: I will present extensions of two classical techniques for modeling dependence in multivariate time series, namely vector autoregressive model (VAR) and coherence analysis. These techniques are applied in describing brain signals dependencies. To generalize the vector autoregressive model, I embedded this model in a mixed effects framework to account for between unit variability. This model is used for exploring multi subject fMRI brain connectivity and identifying connectivity structures with high variability between subjects. To extend the notion of dual frequency coherence developed in the signal processing literature, I will establish the concepts of evolutionary and lagged dual frequency coherence. These concepts were developed with the aim to investigate time dependent brain oscillatory activity between different frequencies and were motivated by empirical evidence that point out how brain processes and mental disorders can be described by interactions between oscillatory neuronal activity at different frequencies.
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