A Multiregression Dynamic Model (MDM) is a class of multivariatetime series that represents various dynamic causal processes in a graphical way.One of the advantages of this class is that, in contrast to many other DynamicBayesian Networks, the hypothesised relationships accommodate conditional conjugateinference. We demonstrate for the first time how straightforward it is tosearch over all possible connectivity networks with dynamically changing intensityof transmission to find the Maximum a Posteriori Probability (MAP) modelwithin this class. This search method is made feasible by using a novel applicationof an Integer Programming algorithm. The efficacy of applying this particularclass of dynamic models to this domain is shown and more specifically the computationalefficiency of a corresponding search of 11-node Directed Acyclic Graph(DAG) model space. We proceed to show how diagnostic methods, analogous tothose defined for static Bayesian Networks, can be used to suggest embellishmentof the model class to extend the process of model selection. All methods are illustratedusing simulated and real resting-state functional Magnetic ResonanceImaging (fMRI) data.