Nonhomogeneous hidden semi-Markov models for toroidal data

A nonhomogeneous hidden semi-Markov model is proposed to segment bivariate time series of wind and wave directions according to a finite number of latent regimes and, simultaneously, estimate the influence of time-varying covariates on the process' survival under each regime. The model is a mixture of toroidal densities, whose parameters depend on the evolution of a semi-Markov chain, which is in turn modulated by time-varying covariates. It includes nonhomogeneous hidden Markov models and hidden semi-Markov models as special cases. Parameter estimates are obtained using an Expectation-Maximization algorithm that relies on an efficient augmentation of the latent process. Fitted on a time series of wind and wave directions recorded in the Adriatic Sea, the model offers a clear-cut description of sea state dynamics in terms of latent regimes and captures the influence of time-varying weather conditions on the duration of such regimes.