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2 Dependence and nonstationarity The asymptotic results introduced in Part 1 have assumed the underlying process to be indepen-

Summary: 2 Dependence and non­stationarity
The asymptotic results introduced in Part 1 have assumed the underlying process to be indepen-
dent and identically distributed (i.i.d.). They also assume this process is stationary. In practice,
extreme value data ­ particularly environmental time series ­ exhibit some form of departure
from this ideal. The most common forms are:
-- Local temporal dependence, where successive values of the time series are dependent, but
values farther apart are independent (to a good approximation);
-- Long term trends, where the underlying distribution changes gradually over time;
-- Seasonal variation, where the underlying distribution changes periodically through time.
These departures can be handled through a combination of extending both the theory and the
modelling. However, although a wide range of theoretical models for non­stationarity have
been studied, only in a few cases have these been used for statistical modelling; the results
have generally been too specific to be of use in modelling data for which the form of non­
stationarity is unknown. Over the last decade or so, it has been more usual for practitioners to
employ statistical procedures which allow the existing results to be applied. In Part 2, we will
consider some of these in detail.
2.1 Extremes of dependent sequences
For the types of data to which extreme value models are commonly applied, temporal indepen-
dence is usually an unrealistic assumption. In particular, extreme conditions often persist over
several consecutive observations, bringing into question the appropriateness of models such as


Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield


Collections: Mathematics