A latent trawl process model for extreme values

TL;DR

This paper introduces a hierarchical trawl process model for extreme values that captures complex temporal dependence in environmental data, allowing flexible marginal and dependence structures aligned with extreme value theory.

Contribution

It develops a novel hierarchical trawl process model for extreme values, accommodating a wide range of marginal distributions and temporal dependence structures.

Findings

Model effectively captures dependence in environmental extremes.

Flexible in modeling generalized Pareto distributions.

Applications demonstrate improved fit to real data.

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 processes, which are stationary, infinitely divisible stochastic processes. The model for extreme values is constructed by embedding a trawl process in a hierarchical framework, which ensures that the marginal distribution is generalised Pareto, as expected from classical 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 marginal and temporal dependence 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.