Least squares estimator for Ornstein–Uhlenbeck processes driven by small fractional Lévy noises

Qingbo Wang, Guangjun Shen and Zhenlong Gao

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 8, 1838-1855

Abstract: In this paper, we study the problem of parameter estimation for the Ornstein–Uhlenbeck processes{dXt=θXtdt+dYt dYt=Ytdt+εdLtd driven by Ornstein–Uhlenbeck processes with small fractional Lévy noises and Yt can be observed, based on discrete high frequency observations at regularly spaced time points {tk=kn, k=1,…,n} on [0,1]. We obtain the consistency as well as the asymptotic behavior of the least squares estimator of the unknown parameter θ when ε→0 and n→∞ simultaneously.

Date: 2021
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DOI: 10.1080/03610926.2019.1653923

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