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

Héctor Araya; Soledad Torres; Ciprian A. Tudor

doi:10.1007/s00362-024-01579-5

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

Héctor Araya, Soledad Torres, Ciprian A. Tudor

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	4745-4766
Number of pages	22
Journal	Statistical Papers
Volume	65
Issue number	7
DOIs	https://doi.org/10.1007/s00362-024-01579-5
State	Published - Sep 2024
Externally published	Yes

Keywords

60G35
60H07
60H15
Hermite process
Multiple Wiener–Itô integrals
Non Gaussian
Ornstein–Uhlenbeck process
Parameter estimation
Small noise

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title = "Least squares estimation for the Ornstein–Uhlenbeck process with small Hermite noise",

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.",

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AU - Araya, Héctor

AU - Torres, Soledad

AU - Tudor, Ciprian A.

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

PY - 2024/9

Y1 - 2024/9

N2 - 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.

AB - 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.

KW - 60G35

KW - 60H07

KW - 60H15

KW - Hermite process

KW - Multiple Wiener–Itô integrals

KW - Non Gaussian

KW - Ornstein–Uhlenbeck process

KW - Parameter estimation

KW - Small noise

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SP - 4745

EP - 4766

JO - Statistical Papers

JF - Statistical Papers

IS - 7

ER -

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

Abstract

Keywords

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