  We introduce the minimal maximally predictive models ({\epsilon}-machines) of
processes generated by certain hidden semi-Markov models. Their causal states
are either hybrid discrete-continuous or continuous random variables and
causal-state transitions are described by partial differential equations.
Closed-form expressions are given for statistical complexities, excess
entropies, and differential information anatomy rates. We present a complete
analysis of the {\epsilon}-machines of continuous-time renewal processes and,
then, extend this to processes generated by unifilar hidden semi-Markov models
and semi-Markov models. Our information-theoretic analysis leads to new
expressions for the entropy rate and the rates of related information measures
for these very general continuous-time process classes.
