Least squares estimation for the Ornstein–Uhlenbeck process with small Hermite noise

Héctor Araya (), Soledad Torres () and Ciprian A. Tudor ()
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Héctor Araya: Universidad Adolfo Ibañez
Soledad Torres: Universidad de Valparaíso
Ciprian A. Tudor: Université de Lille 1

Statistical Papers, 2024, vol. 65, issue 7, No 25, 4745-4766

Abstract: Abstract We consider the problem of the drift parameter estimation for a non-Gaussian long memory Ornstein–Uhlenbeck process driven by a Hermite process. To estimate the unknown parameter, discrete time high-frequency observations at regularly spaced time points and the least squares estimation method are used. By means of techniques based on Wiener chaos and multiple stochastic integrals, the consistency and the limit distribution of the least squares estimator of the drift parameter have been established. To show the computational implementation of the obtained results, different simulation examples are given.

Keywords: Non Gaussian; Hermite process; Parameter estimation; Multiple Wiener–Itô integrals; Ornstein–Uhlenbeck process; Small noise; 60H15; 60H07; 60G35 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01579-5

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