Hidden semi-Markov models with inhomogeneous state dwell-time distributions

The well-established methodology for the estimation of hidden semi-Markov models (HSMMs) as hidden Markov models (HMMs) with extended state spaces is further developed. Covariate influences are incorporated across all aspects of the state process model, in particular regarding the distributions governing the state dwell time. The special case of periodically varying covariate effects on the state dwell-time distributions — and possibly the conditional transition probabilities — is examined in detail. Important properties of these models are derived, including the periodically varying unconditional state distribution as well as the overall state dwell-time distribution. Simulation studies are conducted to assess key properties of these models and provide recommendations for hyperparameter settings. A case study involving an HSMM with periodically varying dwell-time distributions is presented to analyse the movement trajectory of an Arctic muskox, demonstrating the practical relevance of the developed methodology.