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