  Markov switching models (MSMs) are probabilistic models that employ multiple
sets of parameters to describe different dynamic regimes that a time series may
exhibit at different periods of time. The switching mechanism between regimes
is controlled by unobserved random variables that form a first-order Markov
chain. Explicit-duration MSMs contain additional variables that explicitly
model the distribution of time spent in each regime. This allows to define
duration distributions of any form, but also to impose complex dependence
between the observations and to reset the dynamics to initial conditions.
Models that focus on the first two properties are most commonly known as hidden
semi-Markov models or segment models, whilst models that focus on the third
property are most commonly known as changepoint models or reset models. In this
monograph, we provide a description of explicit-duration modelling by
categorizing the different approaches into three groups, which differ in
encoding in the explicit-duration variables different information about regime
change/reset boundaries. The approaches are described using the formalism of
graphical models, which allows to graphically represent and assess statistical
dependence and therefore to easily describe the structure of complex models and
derive inference routines. The presentation is intended to be pedagogical,
focusing on providing a characterization of the three groups in terms of model
structure constraints and inference properties. The monograph is supplemented
with a software package that contains most of the models and examples
described. The material presented should be useful to both researchers wishing
to learn about these models and researchers wishing to develop them further.
