Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter

Yaozhong Hu (), David Nualart () and Hongjuan Zhou ()
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Yaozhong Hu: University of Alberta
David Nualart: University of Kansas
Hongjuan Zhou: University of Kansas

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 1, No 5, 142 pages

Abstract: Abstract This paper studies the least squares estimator (LSE) for the drift parameter of an Ornstein–Uhlenbeck process driven by fractional Brownian motion, whose observations can be made either continuously or at discrete time instants. A central limit theorem is proved when the Hurst parameter $$H \in (0, 3/4]$$ H ∈ ( 0 , 3 / 4 ] and a noncentral limit theorem is proved for $$H\in (3/4, 1)$$ H ∈ ( 3 / 4 , 1 ) . Thus, the open problem left in the previous paper (Hu and Nualart in Stat Probab Lett 80(11–12):1030–1038, 2010) is completely solved, where a central limit theorem for the least squares estimator is proved for $$H\in [1/2, 3/4)$$ H ∈ [ 1 / 2 , 3 / 4 ) . The LSE is then used to study the asymptotics for other alternative estimators, such as the ergodic type estimator.

Keywords: Fractional Brownian motion; Fractional Ornstein–Uhlenbeck processes; Parameter estimation; Fourth moment theorem; Central limit theorem; Noncentral limit theorem (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (16)

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DOI: 10.1007/s11203-017-9168-2

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