  State-switching models such as hidden Markov models or Markov-switching
regression models are routinely applied to analyse sequences of observations
that are driven by underlying non-observable states. Coupled state-switching
models extend these approaches to address the case of multiple observation
sequences whose underlying state variables interact. In this paper, we provide
an overview of the modelling techniques related to coupling in state-switching
models, thereby forming a rich and flexible statistical framework particularly
useful for modelling correlated time series. Simulation experiments demonstrate
the relevance of being able to account for an asynchronous evolution as well as
interactions between the underlying latent processes. The models are further
illustrated using two case studies related to a) interactions between a dolphin
mother and her calf as inferred from movement data; and b) electronic health
record data collected on 696 patients within an intensive care unit.
