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Resumo(s)
Pareto processes are suitable to model stationary heavy-tailed data. Here, we consider the
auto-regressive Gaver–Lewis Pareto Process and address a study of the tail behavior. We characterize
its local and long-range dependence. We will see that consecutive observations are asymptotically
tail independent, a feature that is often misevaluated by the most common extremal models and
with strong relevance to the tail inference. This also reveals clustering at “penultimate” levels.
Linear correlation may not exist in a heavy-tailed context and an alternative diagnostic tool will
be presented. The derived properties relate to the auto-regressive parameter of the process and
will provide estimators. A comparison of the proposals is conducted through simulation and an
application to a real dataset illustrates the procedure.
Descrição
Palavras-chave
Extreme value theory Autoregressive processes Extremal index Asymptotic tail independence