A multilevel hidden Markov model for space-time cylindrical data

Motivated by segmentation issues in marine studies, a novel hidden Markov model is proposed for the analysis of cylindrical space-time series, that is, bivariate space-time series of intensities and angles. The model is a multilevel mixture of cylindrical densities, where the parameters of the mixture vary at the spatial level according to a latent Markov random field, while the parameters of the hidden Markov random field evolve at the temporal level according to the states of a hidden Markov chain. Due to the numerical intractability of the likelihood function, parameters are estimated by a computationally efficient EM algorithm based on the specification of a weighted composite likelihood. The proposal is tested in a case study that involves speeds and directions of marine currents in the Gulf of Naples.