This paper develops the asymptotic theory for estimators of two parameters in the drift function 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 theory for the persistent parameter depends critically on its sign, corresponding asymptotically to the stationary case, the explosive case, and the null recurrent case. In all three cases, the least squares method is considered. When the persistent parameter is positive, the estimate method of Hu and Nualart (2010) is also considered. The strong consistency and the asymptotic distribution are obtained in all three cases.
Least squares, Fractional Vasicek model, Stationary process, Explosive process, Null recurrent, Strong consistency, Asymptotic distribution
Singapore Management University
City or Country
XIAO, Weilin and YU, Jun.
Asymptotic theory for estimating drift parameters in the fractional Vasicek model. (2017). Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1966
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.