Asymptotic theory for estimating drift parameters in the fractional Vasicek model

This article develops an 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 with long-range dependence is assumed to be driven by a fractional Brownian motion wit...

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Main Authors: XIAO, Weilin, YU, Jun
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2019
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Online Access:https://ink.library.smu.edu.sg/soe_research/2253
https://ink.library.smu.edu.sg/context/soe_research/article/3252/viewcontent/ET_XiaoYu_2019_av.pdf
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spelling sg-smu-ink.soe_research-32522020-07-06T08:22:19Z Asymptotic theory for estimating drift parameters in the fractional Vasicek model XIAO, Weilin YU, Jun This article develops an 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 with long-range dependence is assumed to be driven by a fractional Brownian motion with the Hurst parameter greater than or equal to one half. It is shown that, when the Hurst parameter is known, the asymptotic theory for the persistence 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, and strong consistency and the asymptotic distribution are obtained. When the persistence parameter is positive, the estimation method of Hu and Nualart (2010) is also considered. 2019-02-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2253 info:doi/10.1017/S0266466618000051 https://ink.library.smu.edu.sg/context/soe_research/article/3252/viewcontent/ET_XiaoYu_2019_av.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Least squares Fractional Vasicek model Stationary process Explosive process Null recurrent Strong consistency Asymptotic distribution Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Least squares
Fractional Vasicek model
Stationary process
Explosive process
Null recurrent
Strong consistency
Asymptotic distribution
Econometrics
spellingShingle Least squares
Fractional Vasicek model
Stationary process
Explosive process
Null recurrent
Strong consistency
Asymptotic distribution
Econometrics
XIAO, Weilin
YU, Jun
Asymptotic theory for estimating drift parameters in the fractional Vasicek model
description This article develops an 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 with long-range dependence is assumed to be driven by a fractional Brownian motion with the Hurst parameter greater than or equal to one half. It is shown that, when the Hurst parameter is known, the asymptotic theory for the persistence 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, and strong consistency and the asymptotic distribution are obtained. When the persistence parameter is positive, the estimation method of Hu and Nualart (2010) is also considered.
format text
author XIAO, Weilin
YU, Jun
author_facet XIAO, Weilin
YU, Jun
author_sort XIAO, Weilin
title Asymptotic theory for estimating drift parameters in the fractional Vasicek model
title_short Asymptotic theory for estimating drift parameters in the fractional Vasicek model
title_full Asymptotic theory for estimating drift parameters in the fractional Vasicek model
title_fullStr Asymptotic theory for estimating drift parameters in the fractional Vasicek model
title_full_unstemmed Asymptotic theory for estimating drift parameters in the fractional Vasicek model
title_sort asymptotic theory for estimating drift parameters in the fractional vasicek model
publisher Institutional Knowledge at Singapore Management University
publishDate 2019
url https://ink.library.smu.edu.sg/soe_research/2253
https://ink.library.smu.edu.sg/context/soe_research/article/3252/viewcontent/ET_XiaoYu_2019_av.pdf
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