Least-squares estimation for the Vasicek model driven by the complex fractional Brownian motion. Issue 4 (19th May 2022)

• Record Type: Journal Article
• Authors: Shen, Guangjun; Tang, Zheng; Yin, Xiuwei
• Is Part Of: Stochastics. Volume 94:Issue 4(2022)
• Page Start: 537
• Page End: 558
• Publication Date: 2022-05-19
• Subjects: Fractional Brownian motion -- complex multiple Wiener–Itô integral -- least-squares estimator -- fourth moment theorems -- consistency -- asymptotic normality; 60G15 -- 60G18 -- 60G22 -- 60H07; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2021.1959587
• Languages: English
• ISSNs: 1744-2508

Abstract

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.