Non-homogeneous Markov Mixture of Periodic Autoregressions for the Analysis of Air Pollution in the Lagoon of Venice

Markov mixtures of autoregressions (MMAR) have been recently used to analyse the behaviour of non-linear and non-Gaussian time series. A special MMAR model with periodic components and a non-homogeneous hidden Markov chain is proposed here: the transition probabilities of the hidden chain are timevarying, because they depend, through logistic functions, on the dynamics of exogenous variables. We perform a complete Metropolis-within-Gibbs algorithm associated to the random permutation sampling for model choice and variable selection and to constrained permutation sampling for the estimation of the unknown parameters and the latent data. An environmental application is developed on the series of sulphur dioxide and meteorological variables recorded by an air pollution testing station in the lagoon of Venice.