Explicit-Duration Markov Switching Models

Markov switching models MSMs are probabilistic models that employmultiple sets of parameters to describe different dynamic regimesthat a time series may exhibit at different periods of time. Theswitching mechanism between regimes is controlled by unobserved randomvariables that form a first-order Markov chain. Explicit-durationMSMs contain additional variables that explicitly model the distributionof time spent in each regime. This allows to define duration distributionsof any form, but also to impose complex dependence betweenthe observations and to reset the dynamics to initial conditions. Modelsthat focus on the first two properties are most commonly known as hiddensemi-Markov models or segment models, whilst models that focuson the third property are most commonly known as changepoint modelsor reset models. In this monograph, we provide a description of explicitdurationmodelling by categorizing the different approaches into threegroups, which differ in encoding in the explicit-duration variables differentinformation about regime change/reset boundaries. The approachesare described using the formalism of graphical models, which allows tographically represent and assess statistical dependence and thereforeto easily describe the structure of complex models and derive inferenceroutines. The presentation is intended to be pedagogical, focusingon providing a characterization of the three groups in terms of modelstructure constraints and inference properties. The monograph is supplementedwith a software package that contains most of the modelsand examples described. The material presented should be useful toboth researchers wishing to learn about these models and researcherswishing to develop them further.The supplementary data for this issue will be available soon.