YUIMA

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.


References in zbMATH (referenced in 12 articles , 2 standard articles )

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  1. Bajja, Salwa; Es-Sebaiy, Khalifa; Viitasaari, Lauri: Least squares estimator of fractional Ornstein-Uhlenbeck processes with periodic mean (2017)
  2. Charles Driver and Johan Oud and Manuel Voelkle: Continuous Time Structural Equation Modeling with R Package ctsem (2017)
  3. Long, Hongwei; Ma, Chunhua; Shimizu, Yasutaka: Least squares estimators for stochastic differential equations driven by small Lévy noises (2017)
  4. Viitasaari, Lauri: Representation of stationary and stationary increment processes via Langevin equation and self-similar processes (2016)
  5. Ana Cebrián; Jesús Abaurrea; Jesús Asín: NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes (2015)
  6. Azmoodeh, Ehsan; Viitasaari, Lauri: Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind (2015)
  7. Iacus, Stefano M.; Mercuri, Lorenzo: Implementation of Lévy CARMA model in yuima package (2015)
  8. 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)
  9. 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)
  10. Barndorff-Nielsen, Ole E.; Pakkanen, Mikko S.; Schmiegel, Jürgen: Assessing relative volatility/ intermittency/energy dissipation (2014)
  11. Brouste, Alexandre; Iacus, Stefano M.: Parameter estimation for the discretely observed fractional Ornstein-Uhlenbeck process and the Yuima R package (2013)
  12. Alexandre Brouste, Stefano M. Iacus: Parameter estimation for the discretely observed fractional Ornstein-Uhlenbeck process and the Yuima R package (2011) arXiv