Fractionally integrated moving average stable processes with long-range dependence
dc.contributor.author | Feltes, Guilherme de Lima | pt_BR |
dc.contributor.author | Lopes, Silvia Regina Costa | pt_BR |
dc.date.accessioned | 2022-08-16T04:47:02Z | pt_BR |
dc.date.issued | 2022 | pt_BR |
dc.identifier.issn | 1980-0436 | pt_BR |
dc.identifier.uri | http://hdl.handle.net/10183/246957 | pt_BR |
dc.description.abstract | Long memory processes driven by Lévy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function that decays like a power function. Here, we study a class of Lévy processes whose second-order moments are infinite, the so-called α-stable processes. Based on Samorodnitsky and Taqqu (1994), we construct an isometry that allows us to define stochastic integrals concerning the linear fractional stable motion using Riemann-Liouville fractional integrals. With this construction, an integration by parts formula follows naturally. We then present a family of stationary SαS processes with the property of long-range dependence, using a generalized measure to investigate its dependence structure. At the end, the law of large number’s result for a time’s sample of the process is shown as an application of the isometry and integration by parts formula. | en |
dc.format.mimetype | application/pdf | pt_BR |
dc.language.iso | eng | pt_BR |
dc.relation.ispartof | ALEA - Latin American Journal of Probability and Mathematical Statistics. Rio de janeiro. Vol. 19, (2022), p. 599 - 615 | pt_BR |
dc.rights | Open Access | en |
dc.subject | Dependência de longo alcance | pt_BR |
dc.subject | Fractionally integrated moving average stable processes | en |
dc.subject | Processo de levy | pt_BR |
dc.subject | Long-range dependence | en |
dc.subject | Isometrias | pt_BR |
dc.subject | Linear fractional stable motion | en |
dc.title | Fractionally integrated moving average stable processes with long-range dependence | pt_BR |
dc.type | Artigo de periódico | pt_BR |
dc.identifier.nrb | 001140999 | pt_BR |
dc.type.origin | Nacional | pt_BR |
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