Least squares estimation for fractional Brownian bridge with linear drift

Jingqi Han, Yaqin Sun and Litan Yan

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 21, 6735-6760

Abstract: In this article, we research the asymptotic properties of least squares estimation for fractional Brownian bridge with linear drift dXt=α(θ−Xt)T−tdt+dBtH, 0≤t 0,θ∈R and γ≜αθ are unknown parameters, BH is fractional Brownian motion with Hurst index H∈(1/2,1), as well as T > 0. Based on the continuous-time observation, we obtain the estimators α̂,γ̂ and θ̂ for α, γ, and θ. Depending on the value of α, we can have the strong consistency or not as t→T. Since these estimates do not formally depend on the value of θ, we also get the rate of these convergences when the consistency holds in both θ≠0 and θ = 0 case. This work extends the results of Es-Sebaiy and Nourdin (2013) studied in the case where θ = 0 is known.

Date: 2025
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DOI: 10.1080/03610926.2025.2461615

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