In this dissertation, we develop a cluster of models for high dimensional time dependent data with a hierarchical structure observed in resting state functional magnetic resonance imaging data. Addressing some of the existing fundamental concerns, we incorporate a flexible spatio type covariance matrix when distance-based space is absent and ensure its positive definiteness. Furthermore, we reduce the dimension using Moran basis functions for easing the computational burden while guaranteeing robust estimates. This is achieved by developing a spatio type weighting matrix utilizing the semivariogram. In multiple ways, we can count the benefits of our approach. First, the hierarchical nature of the proposed spatiotemporal model reduces the noise at different levels, leading to better power in signal detection. Second, our approach decorrelates the temporal association for proper inferential properties and explores the input-output relation focusing on only spatial correlations. Third, it provides better interpretation of the relationship between outcome measures and covariates while controlling the false discovery rate. Methodologies developed in this article are used to detect disrupted connectivities from neuroimaging data comparing autism subjects to controls. A network is built using disrupted connectivities and interpretation of links is provided in terms of neurobehavioral functions
