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

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