Next Article in Journal
Implied Distributions from GBPUSD Risk-Reversals and Implication for Brexit Scenarios
Previous Article in Journal
Effects of Gainsharing Provisions on the Selection of a Discount Rate for a Defined Benefit Pension Plan
Article

Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective

by 1,2,3,* and 4
1
Centro de Matemática da Universidade do Minho, Campus de Gualtar 4710-057 Braga, Portugal
2
Centro de Matemática Computacional e Estocástica, Departamento de Matemática-Instituto Superior Técnico Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
3
Centro de Estatística e Aplicações, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
4
Universidade da Beira Interior, Centro de Matemática e Aplicações (CMA-UBI), Avenida Marquês d’Avila e Bolama, Covilhã 6200-001, Portugal
*
Author to whom correspondence should be addressed.
Academic Editor: Mogens Steffensen
Risks 2017, 5(3), 33; https://doi.org/10.3390/risks5030033
Received: 10 April 2017 / Revised: 14 June 2017 / Accepted: 16 June 2017 / Published: 27 June 2017
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. View Full-Text
Keywords: extreme value theory; autoregressive processes; extremal index; asymptotic tail independence extreme value theory; autoregressive processes; extremal index; asymptotic tail independence
Show Figures

Figure 1

MDPI and ACS Style

Ferreira, M.; Ferreira, H. Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective. Risks 2017, 5, 33. https://doi.org/10.3390/risks5030033

AMA Style

Ferreira M, Ferreira H. Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective. Risks. 2017; 5(3):33. https://doi.org/10.3390/risks5030033

Chicago/Turabian Style

Ferreira, Marta, and Helena Ferreira. 2017. "Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective" Risks 5, no. 3: 33. https://doi.org/10.3390/risks5030033

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop