Least squares estimator for Ornstein–Uhlenbeck processes driven by fractional Lévy processes from discrete observations

Guangjun Shen () and Qian Yu ()
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Guangjun Shen: Anhui Normal University
Qian Yu: Anhui Normal University

Statistical Papers, 2019, vol. 60, issue 6, No 19, 2253-2271

Abstract: Abstract In this paper, we consider the problem of parameter estimation for Ornstein–Uhlenbeck processes with small fractional Lévy noises, based on discrete observations at n regularly spaced time points $$t_i=i/n,$$ t i = i / n , $$i=1,\ldots ,n$$ i = 1 , … , n on [0, 1]. Least squares method is used to obtain an estimator of the drift parameter. The consistency and the asymptotic distribution of the estimator have been established.

Keywords: Ornstein–Uhlenbeck processes; Fractional Lévy processes; Least squares estimator; Asymptotic distribution; 60G18; 65C30; 93E24 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00362-017-0918-4

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