There is a rising interest in studying the degree of connection and the causal relationships between brain regions, as a growing body of evidence suggests that features of these interactions could play a role as markers in a host of neurological diseases. The vast majority of brain connectivity studies treats the brain network as stationary. New insights on the temporal behaviour of these connections could significantly improve our understanding of brain networking in both physiology and pathology. In this paper, we propose the application of a computational methodology, named Particle Filter (PF), to functional Magnetic Resonance Imaging (fMRI) data. The PF algorithm aims to estimate time-varying hidden variables of a given observational model through a Sequential Monte Carlo approach. The fMRI data are represented as a first-order linear time-varying Vector Autoregression model (VAR). On simulated time series, the PF approach effectively detected and enabled to follow time-varying hidden parameters and it captured causal relationships among signals. The method was also applied to real fMRI data and provided similar results to those obtained by using a different proxy measure of causal dependency, that is, correlation between delayed time series. Interestingly, the PF approach also enabled to detect statistically significant changes in the cause-effect relationships between areas, which correlated with the underlying stimulation pattern delivered to subjects during the fMRI acquisition.