Fractionally integrated moving average stable processes with long-range dependence
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Data
2022Tipo
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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 ...
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. ...
Contido em
ALEA - Latin American Journal of Probability and Mathematical Statistics. Rio de janeiro. Vol. 19, (2022), p. 599 - 615
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Artigos de Periódicos (39401)Ciências Exatas e da Terra (5976)
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