Asymptotic theory for quadratic variation of harmonizable fractional stable processes

Andreas Basse-O’connor; Mark Podolskij

doi:10.1090/tpms/1203

Asymptotic theory for quadratic variation of harmonizable fractional stable processes

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

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Abstract

In this paper we study the asymptotic theory for quadratic variation of a harmonizable fractional α-stable process. We show a law of large numbers with a non-ergodic limit and obtain weak convergence towards a Lévy-driven Rosenblatt random variable when the Hurst parameter satisfies H ∈ (1/2, 1) and α(1−H) < 1/2. This result complements the asymptotic theory for fractional stable processes.

Originalsprog	Engelsk
Tidsskrift	Theory of Probability and Mathematical Statistics
Vol/bind	110
Sider (fra-til)	3-12
Antal sider	10
ISSN	0094-9000
DOI	https://doi.org/10.1090/tpms/1203
Status	Udgivet - 2024

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abstract = "In this paper we study the asymptotic theory for quadratic variation of a harmonizable fractional α-stable process. We show a law of large numbers with a non-ergodic limit and obtain weak convergence towards a L{\'e}vy-driven Rosenblatt random variable when the Hurst parameter satisfies H ∈ (1/2, 1) and α(1−H) < 1/2. This result complements the asymptotic theory for fractional stable processes.",

keywords = "Fractional processes, harmonizable processes, limit theorems, quadratic vari-ation, stable L{\'e}vy motion",

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AU - Podolskij, Mark

PY - 2024

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N2 - In this paper we study the asymptotic theory for quadratic variation of a harmonizable fractional α-stable process. We show a law of large numbers with a non-ergodic limit and obtain weak convergence towards a Lévy-driven Rosenblatt random variable when the Hurst parameter satisfies H ∈ (1/2, 1) and α(1−H) < 1/2. This result complements the asymptotic theory for fractional stable processes.

AB - In this paper we study the asymptotic theory for quadratic variation of a harmonizable fractional α-stable process. We show a law of large numbers with a non-ergodic limit and obtain weak convergence towards a Lévy-driven Rosenblatt random variable when the Hurst parameter satisfies H ∈ (1/2, 1) and α(1−H) < 1/2. This result complements the asymptotic theory for fractional stable processes.

KW - Fractional processes

KW - harmonizable processes

KW - limit theorems

KW - quadratic vari-ation

KW - stable Lévy motion

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JO - Theory of Probability and Mathematical Statistics

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ER -

Asymptotic theory for quadratic variation of harmonizable fractional stable processes

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