Capability of detecting causal or effective connectivity from resting-state functional magnetic resonance imaging (R-fMRI) is highly desirable for better understanding the cooperative nature of the brain. Effective connectivity provides specific dynamic temporal information of R-fMRI time series and reflects the directional causal influence of one brain region over another. These causal influences among brain regions are normally extracted based on the concept of Granger causality. Conventionally, the effective connectivity is inferred using multivariate autoregressive (MAR) modeling with default model order q = 1, considering low frequency fluctuation of R-fMRI time series. This assumption, although reduces the modeling complexity, does not guarantee the best fitting of R-fMRI time series at different brain regions. Instead of using the default model order, we propose to estimate the optimal model order based upon MAR order distribution to better characterize these causal influences at each brain region. Due to sparse nature of brain connectivity networks, an orthogonal least square (OLS) regression algorithm is incorporated to MAR modeling to minimize spurious effective connectivity. Effective connectivity networks inferred using the proposed optimal sparse MAR modeling are applied to Mild Cognitive Impairment (MCI) identification and obtained promising results, demonstrating the importance of using optimal causal relationships between brain regions for neurodegeneration disorder identification.