  For a network of discrete states with a periodically driven Markovian
dynamics, we develop an inference scheme for an external observer who has
access to some transitions. Based on waiting-time distributions between these
transitions, the periodic probabilities of states connected by these observed
transitions and their time-dependent transition rates can be inferred.
Moreover, the smallest number of hidden transitions between accessible ones and
some of their transition rates can be extracted. We prove and conjecture lower
bounds on the total entropy production for such periodic stationary states.
Even though our techniques are based on generalizations of known methods for
steady states, we obtain original results for those as well.
