Maximum likelihood estimation for the fractional Vasicek model

Maximum likelihood estimation for the fractional Vasicek model

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 estima...

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Bibliographic Details
Main Authors: TANAKA, Katsuto, XIAO, Weilin, YU, Jun
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2019
Subjects:
Maximum likelihood estimate
Fractional Vasicek model
Asymptotic distribution
Stationary process
Explosive process
Null recurrent process
Economic Theory
Online Access:https://ink.library.smu.edu.sg/soe_research/2248
https://ink.library.smu.edu.sg/context/soe_research/article/3247/viewcontent/MLEfVm11_.pdf
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Institution: Singapore Management University
Language: English
Description
Summary: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.

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