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Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective

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  • Marta Ferreira

    (Centro de Matemática da Universidade do Minho, Campus de Gualtar 4710-057 Braga, Portugal
    Centro de Matemática Computacional e Estocástica, Departamento de Matemática-Instituto Superior Técnico Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
    Centro de Estatística e Aplicações, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal)

  • Helena Ferreira

    (Universidade da Beira Interior, Centro de Matemática e Aplicações (CMA-UBI), Avenida Marquês d’Avila e Bolama, Covilhã 6200-001, Portugal)

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.

Suggested Citation

  • Marta Ferreira & Helena Ferreira, 2017. "Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective," Risks, MDPI, vol. 5(3), pages 1-12, June.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:3:p:33-:d:102833
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    References listed on IDEAS

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    1. Jennifer L. Wadsworth & Jonathan A. Tawn, 2012. "Dependence modelling for spatial extremes," Biometrika, Biometrika Trust, vol. 99(2), pages 253-272.
    2. Ferreira, Helena & Ferreira, Marta, 2014. "Extremal behavior of pMAX processes," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 46-57.
    3. Ferreira, Helena & Ferreira, Marta, 2015. "Extremes of scale mixtures of multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 82-99.
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