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February 2020 Estimation of the linear fractional stable motion
Stepan Mazur, Dmitry Otryakhin, Mark Podolskij
Bernoulli 26(1): 226-252 (February 2020). DOI: 10.3150/19-BEJ1124

Abstract

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 $\sigma>0$, the self-similarity parameter $H\in(0,1)$ and the stability index $\alpha\in(0,2)$ 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 $(\sigma,\alpha,H)$. We present the law of large numbers and some fully feasible weak limit theorems.

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Stepan Mazur. Dmitry Otryakhin. Mark Podolskij. "Estimation of the linear fractional stable motion." Bernoulli 26 (1) 226 - 252, February 2020. https://doi.org/10.3150/19-BEJ1124

Information

Received: 1 June 2018; Revised: 1 February 2019; Published: February 2020
First available in Project Euclid: 26 November 2019

zbMATH: 07140498
MathSciNet: MR4036033
Digital Object Identifier: 10.3150/19-BEJ1124

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 1 • February 2020
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