 Parameter estimation for the complex fractional Ornstein–Uhlenbeck processes with Hurst parameter H∈(0,12)Fares Alazemi, Abdulaziz Alsenafi, Yong Chen and Hongjuan Zhou Chaos, Solitons & Fractals, 2024, vol. 188, issue C Abstract: We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein–Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen et al. (2017) to the case of Hurst parameter H∈(14,12) and the results of Hu et al. (2019) to a two-dimensional case. When H∈(0,14], it is found that the integrand of the estimator is not in the domain of the standard divergence operator. To facilitate the proofs, we develop a new inner product formula for functions of bounded variation in the reproducing kernel Hilbert space of fractional Brownian motion with Hurst parameter H∈(0,12). This formula is also applied to obtain the second moments of the so-called α-order fractional Brownian motion and the α-fractional bridges with the Hurst parameter H∈(0,12). Keywords: Complex Wiener–Itô multiple integral; Fractional Brownian motion; Fractional Ornstein–Uhlenbeck process; Least squares estimate; Fourth moment theorem; α-fractional Brownian bridge; α-order fractional Brownian motion (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924011081 DOI: 10.1016/j.chaos.2024.115556 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.