I am attempting to model some economic data. Basic measurements
show that a pure-Markov approach will not be appropriate (i.e.
transitions out of a given state are not geometrically distributed.) I
know there exist some methods for dealing with stochastic processes when
the Markov assumption does not strictly hold, including...
Hidden Markov models,
Semi-Markov models,
The "Device of Stages", from Cox and Miller's "Theory of Stochastic
Processes".
My questions are:
1. What are the best standard references on Hidden- and Semi-
Markov models and their applications?
2. Are there any established criteria for determining when a hidden
Markov model would be more appropriate than a semi-Markov model, and
vice versa.
3. Is the "Device of Stages" known by some other name? Cox and
Miller's description makes it sound like it is at least related to
semi-Markov methods.
-- Andrew
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