Spatio-temporal pareto modelling of heavy-tail data

In this work we introduce a spatio-temporal process with pareto marginal distributions. Dependence in space and time is introduced through the use of latent variables in a hierarchical fashion. For some specifications the process becomes strictly stationary in space and time. We present the construction of the process and study some of its properties and dependence measures such as correlation and tail dependence. We follow a Bayesian approach to estimate model parameters and show how to obtain posterior inference via MCMC methods. The performance of the process is illustrated with a pollution dataset of monthly maxima ozone concentrations over the metropolitan area of Mexico City. Our results show that our model is in many instances, superior to a couple of alternative models based on the generalized extreme value distribution.