Publication Type
Working Paper
Version
publishedVersion
Publication Date
3-2019
Abstract
This paper is concerned about the problem of estimating the drift parameters in the fractional Vasicek model from a continuous record of observations. Based on the Girsanov theorem for the fractional Brownian motion, the maximum likelihood (ML) method is used. The asymptotic theory for the ML estimates (MLE) is established in the stationary case, the explosive case, and the null recurrent case for the entire range of the Hurst parameter, providing a complete treatment of asymptotic analysis. It is shown that changing the sign of the persistence parameter will change the asymptotic theory for the MLE, including the rate of convergence and the limiting distribution. It is also found that the asymptotic theory depends on the value of the Hurst parameter.
Keywords
Maximum likelihood estimate, Fractional Vasicek model, Asymptotic distribution, Stationary process, Explosive process, Null recurrent process
Discipline
Economic Theory
Research Areas
Economic Theory
First Page
1
Last Page
31
Publisher
SMU Economics and Statistics Working Paper Series, Paper No. 08-2019
Citation
TANAKA, Katsuto; XIAO, Weilin; and YU, Jun.
Maximum likelihood estimation for the fractional Vasicek model. (2019). 1-31.
Available at: https://ink.library.smu.edu.sg/soe_research/2248
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.