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Asymptotic Theory for Estimating Drift Parameters in the Fractional Vasicek Model

Weilin Xiao () and Jun Yu ()
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Weilin Xiao: School of Management, Zhejiang University

No 8-2017, Economics and Statistics Working Papers from Singapore Management University, School of Economics

Abstract: This paper develops the 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 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 theory for the persistent 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. When the persistent parameter is positive, the estimate method of Hu and Nualart (2010) is also considered. The strong consistency and the asymptotic distribution are obtained in all three cases.

Keywords: Least squares; Fractional Vasicek model; Stationary process; Explosive process; Null recurrent; Strong consistency; Asymptotic distribution (search for similar items in EconPapers)
JEL-codes: C15 C22 G32 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2017-04-27
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-sea
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