Asymptotic Theory for Estimating the Persistent Parameter in the Fractional Vasicek Model

• Main Authors: XIAO, Weilin, Jun YU
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2016
• Subjects: Least squares estimation; Fractional Vasicek model; Stationary process; Explosive process; Consistency; Asymptotic distribution; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1861; https://ink.library.smu.edu.sg/context/soe_research/article/2861/viewcontent/FVasicek05.pdf
• Institution: Singapore Management University

This paper develops the asymptotic theory for the least squares (LS) estimator of the persistent parameter in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model is assumed to be driven by the fractional Brownian motion with a known Hurst parameter greater than or equal to one half. It is shown that the asymptotic properties depend on the sign of the persistent parameter, corresponding to the stationary case, the explosive case and the null recurrent case. The strong consistency and the asymptotic distribution are obtained in all three cases.