A multivariate hidden Markov model for the analysis of space-time circular data

Motivated by issues of marine data analysis under complex orographic conditions, a multivariate hidden Markov model is proposed for the analysis of a temporal sequence of spatial lattice circular data. Each spatial series is modelled by a circular random field whose parameters depend on the evolution of a latent Markov chain. The circular random field is specified in terms of a consistent set of conditional von Mises densities, which are Markov with respect to a spatial neighborhood structure. Because the likelihood of the model depends on a intractable normalizing constant, estimation is based on a computationally efficient EM algorithm that iteratively updates the parameters of a pseudo-likelihood function. The model is illustrated on a space-time series of wintertime wave directions in the Adriatic sea.