  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.
