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2017 Estimation of the Hurst and the stability indices of a $H$-self-similar stable process
Thi To Nhu Dang, Jacques Istas
Electron. J. Statist. 11(2): 4103-4150 (2017). DOI: 10.1214/17-EJS1357

Abstract

In this paper we estimate both the Hurst and the stability indices of a $H$-self-similar stable process. More precisely, let $X$ be a $H$-sssi (self-similar stationary increments) symmetric $\alpha$-stable process. The process $X$ is observed at points $\frac{k}{n}$, $k=0,\ldots,n$. Our estimate is based on $\beta$-negative power variations with $-\frac{1}{2}<\beta<0$. We obtain consistent estimators, with rate of convergence, for several classical $H$-sssi $\alpha$-stable processes (fractional Brownian motion, well-balanced linear fractional stable motion, Takenaka’s process, Lévy motion). Moreover, we obtain asymptotic normality of our estimators for fractional Brownian motion and Lévy motion.

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Thi To Nhu Dang. Jacques Istas. "Estimation of the Hurst and the stability indices of a $H$-self-similar stable process." Electron. J. Statist. 11 (2) 4103 - 4150, 2017. https://doi.org/10.1214/17-EJS1357

Information

Received: 1 April 2017; Published: 2017
First available in Project Euclid: 24 October 2017

zbMATH: 06805088
MathSciNet: MR3715823
Digital Object Identifier: 10.1214/17-EJS1357

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Vol.11 • No. 2 • 2017
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