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Studying brain connectivity has provided new insights to the understanding of brain function. While connectivity measures are conventionally computed from electroencephalogram (EEG) signals directly, the presence of volume conduction represents a serious confound affecting interpretation of results. A common solution is to use a two-stage approach which involves estimating underlying brain sources from scalp EEG recordings and subsequently estimating the connectivity between the inferred sources. Recently, a state-space framework which jointly models the instantaneous mixing effects of volume conduction and the causal relationships between underlying brain sources is proposed. In this paper, we extend the state-space framework and model the source activity by a generalized multivariate autoregressive (mAR) process with possibly non-Gaussian noise. A maximum likelihood estimation approach is developed which allows simultaneous estimation of both the mixing matrix and AR model parameters directly from scalp EEG. The proposed technique was verified with simulated EEG data generated using the single-shell spherical head model and demonstrated improved estimation accuracies compared to conventional two-stage connectivity estimation approaches. Furthermore, the proposed technique was applied to EEG data collected from normal and Parkinson's subjects performing a right-handed force-tracking task with differing amounts of visual feedback. The partial directed coherence (PDC) between sources showed significant differences between groups and conditions. These results suggest that the proposed technique is a powerful method to extract connectivity information from EEG recordings.