Asymptotic Theory for Estimating the Persistent Parameter in the Fractional Vasicek Model

Asymptotic Theory for Estimating the Persistent Parameter in the Fractional Vasicek Model

This paper develops the asymptotic theory for the least squares (LS) estimator of the persistent parameter in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model is assumed to be driven by the fractional Brownian motion with a known Hurst...

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Bibliographic Details
Main Authors: XIAO, Weilin, Jun YU
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2016
Subjects:
Least squares estimation
Fractional Vasicek model
Stationary process
Explosive process
Consistency
Asymptotic distribution
Econometrics
Online Access:https://ink.library.smu.edu.sg/soe_research/1861
https://ink.library.smu.edu.sg/context/soe_research/article/2861/viewcontent/FVasicek05.pdf
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Institution: Singapore Management University
Language: English
Description
Summary:This paper develops the asymptotic theory for the least squares (LS) estimator of the persistent parameter in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model is assumed to be driven by the fractional Brownian motion with a known Hurst parameter greater than or equal to one half. It is shown that the asymptotic properties depend on the sign of the persistent parameter, corresponding to the stationary case, the explosive case and the null recurrent case. The strong consistency and the asymptotic distribution are obtained in all three cases.

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