Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective

Marta Ferreira and Helena Ferreira
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Marta Ferreira: Centro de Matemática da Universidade do Minho, Campus de Gualtar 4710-057 Braga, Portugal
Helena Ferreira: Universidade da Beira Interior, Centro de Matemática e Aplicações (CMA-UBI), Avenida Marquês d’Avila e Bolama, Covilhã 6200-001, Portugal

Risks, 2017, vol. 5, issue 3, 1-12

Abstract: 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.

Keywords: extreme value theory; autoregressive processes; extremal index; asymptotic tail independence (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2017
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