Regression models for time-varying extremes

A common approach to modelling extreme data are to consider the distribution of the exceedance value over a high threshold. This approach is based on the distribution of excess, which follows the generalized Pareto distribution (GPD) and has shown to be adequate for this type of situation. As with all data involving analysis in time, excesses above a threshold may also vary and suffer from the influence of covariates. Thus, the GPD distribution can be modelled by entering the presence of these factors. This paper presents a new model for extreme values, where GPD parameters are written on the basis of a dynamic regression model. The estimation of the model parameters is made under the Bayesian paradigm, with sampling points via MCMC. As with environmental data, behaviour data are related to other factors such as time and covariates such as latitude and distance from the sea. Simulation studies have shown the efficiency and identifiability of the model, and applying real rain data from the state of Piaui, Brazil, shows the advantage in predicting and interpreting the model against other similar models proposed in the literature.