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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.
2020 (English)In: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759, Vol. 26, no 1, p. 226-252Article in journal (Refereed) Published
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 σ>0, the self-similarity parameter H∈(0,1) and the stability index α∈(0,2) of the driving stable motion. The parametric estimation of the model is inspired by the limit theory for stationary increments Lévy moving average processes that has been recently studied in (Ann. Probab. 45 (2017) 4477–4528). More specifically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of (σ,α,H). We present the law of large numbers and some fully feasible weak limit theorems.

Place, publisher, year, edition, pages
The International Statistical Institute, 2020. Vol. 26, no 1, p. 226-252
Keywords [en]
Fractional processes, limit theorems, parametric estimation, stable motion
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:oru:diva-65216DOI: 10.3150/19-BEJ1124ISI: 000499083900008Scopus ID: 2-s2.0-85076579187OAI: oai:DiVA.org:oru-65216DiVA, id: diva2:1185508
Note

Funding Agencies:

Project "Ambit fields: probabilistic properties and statistical inference" - Villum Fonden  

Danmarks Grundforskningsfond

Örebro University  

Project "Models for macro and financial economics after the financial crisis" - Jan Wallander and Tom Hedelius Foundation  P18-0201

Available from: 2018-02-25 Created: 2018-02-25 Last updated: 2022-10-27Bibliographically approved

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Mazur, Stepan

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