{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:13:17Z","timestamp":1760242397121,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,6,27]],"date-time":"2017-06-27T00:00:00Z","timestamp":1498521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Risks"],"abstract":"<jats:p>Pareto processes are suitable to model stationary heavy-tailed data. Here, we consider the auto-regressive Gaver\u2013Lewis 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 \u201cpenultimate\u201d 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.<\/jats:p>","DOI":"10.3390\/risks5030033","type":"journal-article","created":{"date-parts":[[2017,6,28]],"date-time":"2017-06-28T10:25:56Z","timestamp":1498645556000},"page":"33","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Analyzing the Gaver\u2014Lewis Pareto Process under an Extremal Perspective"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7247-3825","authenticated-orcid":false,"given":"Marta","family":"Ferreira","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica da Universidade do Minho, Campus de Gualtar 4710-057 Braga, Portugal"},{"name":"Centro de Matem\u00e1tica Computacional e Estoc\u00e1stica, Departamento de Matem\u00e1tica-Instituto Superior T\u00e9cnico Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal"},{"name":"Centro de Estat\u00edstica e Aplica\u00e7\u00f5es, Faculdade de Ci\u00eancias, Universidade de Lisboa, 1749-016 Lisboa, Portugal"}]},{"given":"Helena","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Universidade da Beira Interior, Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es (CMA-UBI), Avenida Marqu\u00eas d\u2019Avila e Bolama, Covilh\u00e3 6200-001, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,27]]},"reference":[{"key":"ref_1","unstructured":"Shanbhag, D. N., and Rao, C. R. (2001). Pareto Processes. Handbook of Statistics, Elsevier Science B.V."},{"key":"ref_2","unstructured":"Asmussen, Soren (1987). Applied Probability and Queues, John Wiley & Sons."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Beirlant, Jan, Goegebeur, Yuri, Segers, Johan, and Teugels, Jozef (2004). 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