Recent attention has been focused on detecting interregional connectivity in a resting state of the brain, in general, described in terms of functional connectivity based on functional magnetic resonance imaging (fMRI) data. The fMRI functional data are given in the form of multivariate time-series. The authors have proposed a model for the effective connectivity of brain regions based on multivariate autoregressive (MAR) model. MAR modeling allows for the identification of effective connectivity by combining graphical modeling methods with the concept of Granger causality. In our current model, multivariate time-series methods of the brain regions were performed only when the length of the time-series T is sufficiently large. This is opposite of the mechanism used in functional imaging that measures relatively short time-series over thousands of voxels of the brain. As a method of coping with this situation and also in case of sufficiently large T or T <= d (regions), the authors present a novel and highly efficient modeling approach to detect effective connectivity of the brain regions. This proceeds in two steps: (i) accurate estimation of MAR coefficients (paths) using an analytic ridge regression approach, and (ii) network model selection by testing the associated partial correlations. The usefulness of the proposed method is confirmed by the analysis result of simulated and real fMRI experiments, and performance is shown to be high. (C) 2012 Wiley Periodicals, Inc. Concepts Magn Reson Part A 40: 1424, 2012.