Time Varying Structures for Extreme Values

We propose and review different approaches to study non-stationary behavior for extreme values.
We focus on the Generalized Extreme Value (GEV) distribution and use state-space models, and autoregressive structures, to allow for time changes in model parameters. In particular, some of our models are capable of estimating the shape parameter of the GEV distribution in a time-varying fashion. The methodology is illustrated with environmental and meteorological observations of extreme events such as daily maximum ozone levels or annual maximum sea-levels. The different model structures and time-varying parameterizations are compared with Bayesian model selection approaches such as approximate Bayes Factors and the Deviance Information Criteria (DIC). We also review a space-time version that depends on process convolutions and introduce a bivariate representation of extremes with time-varying marginal distributions.