"Estimation of the Hurst and the stability indices of a H-self-similar stable process" (Dang To Nhu, 2017)

Title: Estimation of the Hurst and the stability indices of a H-self-similarstable process

Authors: DANG Thi To Nhu 

Journal: Electronic Journal of Statistics - Vol. 11, Number 2 (2017), 4103-4150.

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 kn, k=0,…,n. Our estimate is based on β-variations with −12<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, L\'evy motion). Moreover, we obtain asymptotic normality of our estimators for fractional Brownian motion and L\'evy motion.