[en] The fractional Ornstein–Uhlenbeck process of the second kind (fOU2) is the solution of the Langevin equation with driving noise where B is a fractional Brownian motion with Hurst parameter H(0, 1). In this article, in the case H>½, we prove that the least-squares estimator introduced in [Hu Y, Nualart D. Parameter estimation for fractional Ornstein–Uhlenbeck processes. Stat. Probab. Lett. 2010;80(11–12):1030–1038], provides a consistent estimator. Moreover, using central limit theorem for multiple Wiener integrals, we prove asymptotic normality of the estimator valid for the whole range H(½, 1).
Disciplines :
Mathematics
Author, co-author :
AZMOODEH, Ehsan ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Morlanes, Jose Igor; Statistiska institutionen, Stockholms Universiet
Language :
English
Title :
Drift parameter estimation for fractional Ornstein–Uhlenbeck process of the second kind
Publication date :
2013
Journal title :
Statistics: A Journal of Theoretical and Applied Statistics
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