  The Dynamic Chain Event Graph (DCEG) is able to depict many classes of
discrete random processes exhibiting asymmetries in their developments and
context-specific conditional probabilities structures. However, paradoxically,
this very generality has so far frustrated its wide application. So in this
paper we develop an object-oriented method to fully analyse a particularly
useful and feasibly implementable new subclass of these graphical models called
the N Time-Slice DCEG (NT-DCEG). After demonstrating a close relationship
between an NT-DCEG and a specific class of Markov processes, we discuss how
graphical modellers can exploit this connection to gain a deep understanding of
their processes. We also show how to read from the topology of this graph
context-specific independence statements that can then be checked by domain
experts. Our methods are illustrated throughout using examples of dynamic
multivariate processes describing inmate radicalisation in a prison.
