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. García, Oscar: Estimating reducible stochastic differential equations by conversion to a least-squares problem (2019)
  2. Bellini, Fabio; Mercuri, Lorenzo; Rroji, Edit: Implicit expectiles and measures of implied volatility (2018)
  3. Feng, Wenfeng; Bailey, Richard M.: Unifying relationships between complexity and stability in mutualistic ecological communities (2018)
  4. Gatheral, Jim; Jaisson, Thibault; Rosenbaum, Mathieu: Volatility is rough (2018)
  5. Iacus, Stefano M.; Yoshida, Nakahiro: Simulation and inference for stochastic processes with YUIMA. A comprehensive R framework for SDEs and other stochastic processes (2018)
  6. Kaino, Yusuke; Uchida, Masayuki: Hybrid estimators for small diffusion processes based on reduced data (2018)
  7. Sun, Lin; Wang, Lin; Fu, Pei: Maximum likelihood estimators of a long-memory process from discrete observations (2018)
  8. Bajja, Salwa; Es-Sebaiy, Khalifa; Viitasaari, Lauri: Least squares estimator of fractional Ornstein-Uhlenbeck processes with periodic mean (2017)
  9. Charles Driver and Johan Oud and Manuel Voelkle: Continuous Time Structural Equation Modeling with R Package ctsem (2017) not zbMATH
  10. Long, Hongwei; Ma, Chunhua; Shimizu, Yasutaka: Least squares estimators for stochastic differential equations driven by small Lévy noises (2017)
  11. Masuda, Hiroki; Uehara, Yuma: Two-step estimation of ergodic Lévy driven SDE (2017)
  12. Stefano Iacus; Lorenzo Mercuri; Edit Rroji: COGARCH(p, q): Simulation and Inference with the yuima Package (2017) not zbMATH
  13. Viitasaari, Lauri: Representation of stationary and stationary increment processes via Langevin equation and self-similar processes (2016)
  14. Ana Cebrián; Jesús Abaurrea; Jesús Asín: NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes (2015) not zbMATH
  15. Azmoodeh, Ehsan; Viitasaari, Lauri: Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind (2015)
  16. Iacus, Stefano M.; Mercuri, Lorenzo: Implementation of Lévy CARMA model in \textttyuimapackage (2015)
  17. Kamatani, Kengo; Uchida, Masayuki: Hybrid multi-step estimators for stochastic differential equations based on sampled data (2015)
  18. Kubilius, Kęstutis; Mishura, Yuliya; Ralchenko, Kostiantyn; Seleznjev, Oleg: Consistency of the drift parameter estimator for the discretized fractional Ornstein-Uhlenbeck process with Hurst index (H\in(0,\frac12)) (2015)
  19. Alexandre Brouste; Masaaki Fukasawa; Hideitsu Hino; Stefano Iacus; Kengo Kamatani; Yuta Koike; Hiroki Masuda; Ryosuke Nomura; Teppei Ogihara; Yasutaka Shimuzu; Masayuki Uchida; Nakahiro Yoshida: The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations (2014) not zbMATH
  20. Barndorff-Nielsen, Ole E.; Pakkanen, Mikko S.; Schmiegel, Jürgen: Assessing relative volatility/ intermittency/energy dissipation (2014)

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