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Maximum Likelihood Estimation for the Fractional Vasicek Model

Katsuto Tanaka (), Weilin Xiao () and Jun Yu ()
Additional contact information
Katsuto Tanaka: Gakushuin University
Weilin Xiao: Zhejiang University

No 8-2019, Economics and Statistics Working Papers from Singapore Management University, School of Economics

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 (search for similar items in EconPapers)
JEL-codes: C15 C22 C32 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2019-03-03
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-sea
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Journal Article: Maximum Likelihood Estimation for the Fractional Vasicek Model (2020) Downloads
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