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 to incorporate covariate influences 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 to derive important properties of such models, namely the periodically varying unconditional state distribution as well as the overall state dwell-time distribution. Through simulation studies, we ascertain key properties of these models and develop recommendations for hyperparameter settings. Furthermore, we provide a case study involving an HSMM with periodically varying dwell-time distributions to analyse the movement trajectory of an arctic muskox, demonstrating the practical relevance of the developed methodology.