Estimation of the Hurst and the stability indices of a H-self-similar stable process

2015/06/18 by Thi To Nhu Dang, Dang, Thi To Nhu, Jacques Istas +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1506.05593

arxiv created 2017/10/18 · arxiv updated 2017/10/19

Abstract

In this paper we estimate both the Hurst and the stable indices of a H-self-similar stable process. More precisely, let X be a H-sssi (self-similar stationary increments) symmetric α-stable process. The process X is observed at points (k)/(n), k=0,…,n. Our estimate is based on β-variations with -(1)/(2)<β<0. We obtain consistent estimators, with rate of convergence, for several classical H-sssi α-stable processes (fractional Brownian motion, well-balanced linear fractional stable motion, Takenaka's processes, Lévy motion). Moreover, we obtain asymptotic normality of our estimators for fractional Brownian motion and Lévy motion. Keywords: H-sssi processes; stable processes; self-similarity parameter estimator; stability parameter estimator.

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