Non-stationary statistical models for extremes: the impact of modelling choices on the description of change

Abstract:

The potential for changes in environmental extremes is routinely investigated by fitting change-permitting extreme value models to long-term observations. In practice, this often entails the use of parametric models in which one or more distribution parameters is allowed to change as a function of time or some other covariate. Changes in the parameter are interpreted as changes in the distribution. Nevertheless, when assessing risk connected to environmental extremes, the main quantity of interest is typically the upper quantiles of the distribution rather than the parameter values. This study investigates the behavior of some metrics which measure the impact of changes in the parameters on quantiles. The mathematical structure of these change metrics for a range of commonly used non-stationary extreme value models is investigated. It is shown that for many common models the predicted changes in the quantiles are a non-intuitive function of the distribution parameters, leading to results which are difficult to interpret and to use for decision-making. It is argued that the decision on which model structure to adopt to describe change in extremes should also take into consideration the types of changes in quantiles which are of interest. Finally, the model structures required to obtain some possibly useful description of change in higher quantiles are presented and exemplified using a dataset of extreme peak river flow measurements in Massachusetts, USA.