Copula-based hidden semi-Markov models for mixed support data

Motivated by a classification problem in directional statistics, we extend the class of hidden semi-Markov models to a copula-based setting. The proposal segments a bivariate time series of mixed support data according to a finite number of latent classes, associated with copula-based densities, simultaneously estimating the distribution of the time spent by the system within each class. The flexibility of the proposed method is illustrated in the non-standard setting of a bivariate time series of mixed observations with a circular and linear support (wave height and direction).