A latent trawl process model for extreme values

Abstract

This paper presents a new model for characterising temporal dependence in exceedances above a threshold. The model is based on the class of trawl pro cesses, which are stationary, infinitely divisible stochastic processes. The model for ex treme values is constructed by embedding a trawl process in a hierarchical framework, whic h ensures that the marginal distribution is generalised Pareto, as expected from class ical extreme value theory. We also consider a modified version of this model that works with a wider class of generalised Pareto distributions, and has the advantage of separating m arginal and temporal depen- dence properties. The model is illustrated by applications to environmental time series, and it is shown that the model offers considerable flexibility in capturing the dependence structure of extreme value data