A Point Process Characterization of Extremes
There are different ways of characterizing the extreme value behavior of a process, and a particularly elegant formulation is derived from the theory of point processes. The mathematics required for a formal treatment of this theory is outside the scope of this book, but we can again give a more informal development. This requires just basic ideas from point process theory. In a sense, the point process characterization leads to nothing new in terms of statistical models; all inferences made using the point process methodology could equally be obtained using an appropriate model from earlier chapters. However, there are two good reasons for considering this approach. First, it provides an interpretation of extreme value behavior that unifies all the models introduced so far; second, the model leads directly to a likelihood that enables a more natural formulation of non-stationarity in threshold excesses than was obtained from the generalized Pareto model discussed in Chapters 4 and 6.
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