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Estimation of the linear fractional stable motion
Örebro University, Örebro University School of Business.
Department of Mathematics, Aarhus University, Aarhus, Denmark.
Department of Mathematics, Aarhus University, Aarhus, Denmark.
2018 (English)Report (Other academic)
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
2018.
Series
Working Papers, School of Business, ISSN 1403-0586 ; 2018:3
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: 2018-02-26Bibliographically approved

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Mazur, Stepan

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