Studying interactions using resting-state functional magnetic resonance imaging (fMRI) signals between discrete brain loci is increasingly recognized as important for understanding normal brain function and may provide insights into many neurodegenerative disorders such as Parkinson's disease (PD). Though much work has been done investigating ways to infer brain connectivity networks, the temporal dynamics of brain coupling has been less well studied. Assuming that brain connections are purely static or purely dynamic is assuredly unrealistic, as the brain must strike a balance between stability and flexibility. In this paper, we propose making joint inference of time-invariant connections as well as time-varying coupling patterns by employing a multitask learning model followed by a least-squares approach to accurately estimate the connectivity coefficients. We applied this method to resting state fMRI data from PD and control subjects and estimated the eigenconnectivity networks to obtain the representative patterns of both static and dynamic brain connectivity features. We found lower network variations in the PD group, which were partially normalized with L-dopa medication, consistent with previous studies suggesting that cognitive inflexibility is characteristic of PD.