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ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL

  • Weilin Xiao (a1) and Jun Yu (a2)
Abstract

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.

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*Address correspondence to Jun Yu, School of Economics and Lee Kong Chian School of Business, Singapore Management University, 90 Stamford Road, Singapore 178903, Singapore; e-mail: yujun@smu.edu.sg.
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We gratefully thank the editor, a co-editor, and two anonymous referees for constructive comments. All errors are our own. Xiao’s research is supported by the Humanities and Social Sciences of Ministry of Education Planning Fund of China (No. 17YJA630114). Yu’s research was supported by the Singapore Ministry of Education (MOE) Academic Research Fund Tier 3 grant MOE2013-T3-1-009.

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Econometric Theory
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