A bayesian dynamic formulation to analyse extreme values

The analysis of extreme values data via classical arguments makes a thorough use of the so called extreme value distribution. An alternative approach, known in the hydrological literature as P.O.T. (Peaks Over Threshold), takes into account the values that exceed a given threshold mark. However, both approaches do not allow for serial dependence in the data. In this paper, we develop forecasting models for extreme values time series. The models use the dynamic linear model as the model formulation and bayesian inference for parameter estimation and updating procedures. They are, therefore, included in the class of bayesian dynamic generalized models for extreme values time series. It is important to mention that the derivation is obtained directly without the use of any kind of numerical approximations, even though the extreme values distribution is not a regular member of the exponential family of distributions. An application is shown, where the problems related to the forecast of extreme values are discussed.