Generalized Pareto models with time-varying tail behavior

In this paper we analyze the extremal events using generalized Pareto distributions (GPD),
allowing the parameters of GPD to vary with time. We use a mixture model that combines
a nonparametric approach for the center and a GPD for the tail of distributions, in which the
uncertainty about the threshold is explicitly considered. We introduce the use of dynamic
linear model (DLM), a very general class of time series models, to model the shape and
scale parameters changes across time. Posterior inference is performed through Markov
Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze
the performance of our proposed model. We also apply the proposed model to three real
financial time series: the Brazilian Vale do Rio Doce, Petrobrás and BOVESPa index, all of
which exhibit several extreme events.