A topic of major current interest in extremevalue analysis
is the investigation of temporal trends. For example, the potential influence
of “greenhouse” effects may result in severe storms becoming
gradually more frequent, or in maximum temperatures gradually increasing, with
time. One approach to evaluating these possibilities is to fit, to data, a
parametric model for temporal parameter variation, as well as a model
describing the marginal distribution of data at any given point in time.
However, structural trend models can be difficult to formulate in many
circumstances, owing to the complex way in which different factors combine to
influence data in the form of extremes. Moreover, it is not advisable to fit
trend models without empirical evidence of their suitability. In this paper,
motivated by datasets on windstorm severity and maximum temperature, we suggest
a nonparametric approach to estimating temporal trends when fitting parametric
models to extreme values from a weakly dependent time series. We illustrate the
method through applications to time series where the marginal distributions are
approximately-Pareto, generalizedPareto, extremevalue or
Gaussian. We introduce timevarying probability plots to assess goodness
of fit, we discuss locallikelihood approaches to fitting the marginal
model within a window and we propose temporal crossvalidation for
selecting window width. In cases where both location and scale are estimated
together, the Gaussian distribution is shown to have special features that
permit it to playa universal role as a “nominal” model for the
marginal distribution.