Parameter estimation for the discretely observed fractional Ornstein-Uhlenbeck process and the Yuima R package. This paper proposes consistent and asymptotically Gaussian estimators for the parameters λ, σ and H of the discretely observed fractional Ornstein-Uhlenbeck process solution of the stochastic differential equation dY t =-λY t dt+σdW t H , where (W t H ,t≥0) is the fractional Brownian motion. For the estimation of the drift λ, the results are obtained only in the case when 1 2<H<3 4. This paper also provides ready-to-use software for the R statistical environment based on the YUIMA package.

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  1. Masuda, Hiroki; Mercuri, Lorenzo; Uehara, Yuma: Noise inference for ergodic Lévy driven SDE (2022)
  2. Shen, Guangjun; Tang, Zheng; Yin, Xiuwei: Least-squares estimation for the Vasicek model driven by the complex fractional Brownian motion (2022)
  3. Haress, El Mehdi; Hu, Yaozhong: Estimation of all parameters in the fractional Ornstein-Uhlenbeck model under discrete observations (2021)
  4. Mercuri, Lorenzo; Perchiazzo, Andrea; Rroji, Edit: Finite mixture approximation of CARMA(p,q) models (2021)
  5. Yu, Qian: Least squares estimator of fractional Ornstein-Uhlenbeck processes with periodic mean for general Hurst parameter (2021)
  6. Arsalane Chouaib Guidoum, Kamal Boukhetala: Performing Parallel Monte Carlo and Moment Equations Methods for Ito and Stratonovich Stochastic Differential Systems: R Package Sim.DiffProc (2020) not zbMATH
  7. Ascione, Giacomo; Mishura, Yuliya; Pirozzi, Enrica: Time-changed fractional Ornstein-Uhlenbeck process (2020)
  8. Kříž, Pavel: A space-consistent version of the minimum-contrast estimator for linear stochastic evolution equations (2020)
  9. Mohammadi, M.; Rezakhah, S.; Modarresi, N.: Semi-Lévy driven continuous-time GARCH process (2020)
  10. Shen, Guang Jun; Wang, Qing Bo; Yin, Xiu Wei: Parameter estimation for the discretely observed vasicek model with small fractional Lévy noise (2020)
  11. Alazemi, F.; Douissi, S.; Es-Sebaiy, Kh.: Berry-Esseen bounds and ASCLTs for drift parameter estimator of mixed fractional Ornstein-Uhlenbeck process with discrete observations. (English. Russian original) (2019)
  12. Chiba, Kohei: Estimation of the lead-lag parameter between two stochastic processes driven by fractional Brownian motions (2019)
  13. Douissi, Soukaina; Es-Sebaiy, Khalifa; Viens, Frederi G.: Berry-Esseen bounds for parameter estimation of general Gaussian processes (2019)
  14. Eguchi, Shoichi; Masuda, Hiroki: Data driven time scale in Gaussian quasi-likelihood inference (2019)
  15. Es-Sebaiy, Khalifa; Viens, Frederi G.: Optimal rates for parameter estimation of stationary Gaussian processes (2019)
  16. Fukasawa, Masaaki; Takabatake, Tetsuya: Asymptotically efficient estimators for self-similar stationary Gaussian noises under high frequency observations (2019)
  17. García, Oscar: Estimating reducible stochastic differential equations by conversion to a least-squares problem (2019)
  18. Hitaj, Asmerilda; Mercuri, Lorenzo; Rroji, Edit: Lévy CARMA models for shocks in mortality (2019)
  19. Liu, Yanghui; Nualart, Eulalia; Tindel, Samy: LAN property for stochastic differential equations with additive fractional noise and continuous time observation (2019)
  20. Rahimi Tabar, M. Reza: Analysis and data-based reconstruction of complex nonlinear dynamical systems. Using the methods of stochastic processes (2019)

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