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Estimation of the linear fractional stable motion
Örebro University, Örebro University School of Business.ORCID iD: 0000-0002-1395-9427
Department of Mathematics, Aarhus University, Aarhus, Denmark.
Department of Mathematics, Aarhus University, Aarhus, Denmark.
2019 (English)In: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759Article in journal (Other academic) Submitted
Abstract [en]

In this paper we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural non-Gaussian analogue of the scaled fractional Brownian motion. It is fully characterised by the scaling parameter > 0, the self-similarity parameter H 2 (0; 1) and the stability index 2 (0; 2) of the driving stable motion. The parametric estimation of the model is inspired by the limit theory for stationary increments L evy moving average processes that has been recently studied in [5]. More specically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of ( ; ;H). We present the law of large numbers and some fully feasible weak limit theorems.

Place, publisher, year, edition, pages
The International Statistical Institute, 2019.
Keywords [en]
Fractional processes, limit theorems, parametric estimation, stable motion
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:oru:diva-65216OAI: oai:DiVA.org:oru-65216DiVA, id: diva2:1185508
Available from: 2018-02-25 Created: 2018-02-25 Last updated: 2019-04-25Bibliographically approved

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Mazur, Stepan

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