Resting-state functional magnetic resonance imaging (rs-fMRI) is one of the promising non-invasive technology that helps in the detection of neurodegenerative and neurological disorders, localisation of the different areas of the brain and understanding the connectivity between them. It involves the acquisition of time series of MR images while the brain is at "resting-state" and serves as a biomarker for various neurological conditions. The acquired resting-state blood-oxygen-level-dependent (BOLD) data, however, can be corrupted with various artefacts (head movements, physiological movements like breathing etc.). Several preprocessing pipelines have been developed to counter the effect of these known artefacts. However, there might be some artefacts that could not have been attenuated from the signal and might lead to incorrect assessment. Therefore, the thesis proposes model-based filtering of the minimally preprocessed (free from known artefacts) resting-state BOLD signal. It was observed that these signals have long memory dependencies. Hence, the usage of autoregressive fractional integrative process filters is proposed for this purpose. Furthermore, the utility of the approach is demonstrated by removing the effect of white noise from a synthetic signal with statistical properties similar to the resting-state BOLD signal. Afterwards, the proposed method is implemented on the minimally preprocessed resting-state BOLD data of 98 subjects from the Human Connectome Project. The results suggest that the proposed filter, in contrast to the low-pass filter, attenuates the higher frequencies but do not eliminate them. Additionally, four different evaluation measures (power spectrum, functional connectivity using Pearson's correlation and coherence, and eigenmode analysis) were considered. The results provide evidence that the proposed method can be used as an additional step in the already existing preprocessing pipeline to mitigate some artefacts that could not have been filtered out. Besides, the results also provide evidence that the proposed scheme is suitable to capture the dynamics of resting-state BOLD signals.