A Hidden Markov Approach To the Analysis of Cylindrical Space-time Series

Motivated by segmentation issues in marine studies, a new hidden Markov model is proposed for the analysis of cylindrical space-time series, that is, bivariate spacetime series of intensities and angles. The model is based on a hierarchical mixture of cylindrical densities, where the parameters of the mixture components vary across space according to a latent Markov eld, whereas the parameters of the latent Markov eld evolve according to the states of a hidden Markov chain. It allows to segment the data within a nite number of latent classes that vary over time and across space and that represent the conditional distributions of the data under speci c environmental conditions, simultaneously accounting for unobserved heterogeneity, spatial and temporal autocorrelation. Further, it parsimoniously accommodates speci c features of environmental cylindrical data, such as circular-linear correlation, multimodality and skewness. Due to the numerical intractability of the likelihood function, parameters are estimated by a computationally ecient EMtype algorithm that iteratively alternates the maximization of a weighted composite likelihood function with weights updating. The eectiveness of the proposal is tested in a case study that involves speeds and directions of marine currents in the Gulf of Naples observed over time, where the model was capable to cluster cylindrical data according to a nite number of latent classes varying over time that are associated with speci c environmental conditions of the sea.