Least-squares estimation for the Vasicek model driven by the complex fractional Brownian motion. Issue 4 (19th May 2022) - Shen, Guangjun; Tang, Zheng; Yin, Xiuwei
Abstract : In this paper, we study the least-squares estimation problem for the Vasicek model 1 d Z t = a ( b − Z t ) d t + d ξ t H, t ≥ 0, driven by the complex fractional Brownian motion ξ t H = B t H, 1 + i B t H, 2 2, where ( B t H, 1, B t H, 2 ) is a two-dimensional fractional Brownian motion with Hurst parameter H ∈ ( 1 2, 3 4 ) . We obtain the strong consistency and asymptotic normality of a ˆ T and b ˆ T using the Garsia–Rodemich–Rumsey inequality and complex fourth moment theorems.