Many studies in the literature have validated the use of resting-state fMRI (rs-fMRI) for brain disorder/disease identification. Unlike the existing methods that mostly first estimate functional connectivity and then extract features with a graph theory, in this paper, we propose a novel method that directly models the temporal stochastic patterns inherent in BOLD signals for each Region Of Interest (ROI) individually. Specifically, we model temporal BOLD signal fluctuation of an individual ROI by means of Hidden Markov Models (HMMs), and then compute a regional BOLD signal likelihood with the trained HMMs. By regarding the BOLD signal likelihood of ROIs over a whole brain as features, we build a classifier that can discriminate subjects with Autism Spectrum Disorder (ASD) from Normal healthy Controls (NC). In addition, we also devise a method to further investigate the characteristics of temporal dynamics in rs-fMRI estimated by HMMs. For group comparison, we use the metrics of state occupancy rate and lifetime of the optimal hidden states that best represent the temporal BOLD signals. In our experiments with ABIDE cohort, we validated the effectiveness of the proposed method by achieving the highest diagnostic accuracies among competing methods. We could also identify the group differences in temporal dynamics between ASD and NC in terms of state occupancy rate and lifetime of individual states.