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

Author

Listed:
  • Héctor Araya

    (Universidad Adolfo Ibañez)

  • Soledad Torres

    (Universidad de Valparaíso)

  • Ciprian A. Tudor

    (Université de Lille 1)

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.

Suggested Citation

  • Héctor Araya & Soledad Torres & Ciprian A. Tudor, 2024. "Least squares estimation for the Ornstein–Uhlenbeck process with small Hermite noise," Statistical Papers, Springer, vol. 65(7), pages 4745-4766, September.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:7:d:10.1007_s00362-024-01579-5
    DOI: 10.1007/s00362-024-01579-5
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    References listed on IDEAS

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    8. Masayuki Uchida, 2004. "Estimation for Discretely Observed Small Diffusions Based on Approximate Martingale Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 553-566, December.
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