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The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations

Author

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  • Brouste, Alexandre
  • Fukasawa, Masaaki
  • Hino, Hideitsu
  • Iacus, Stefano
  • Kamatani, Kengo
  • Koike, Yuta
  • Masuda, Hiroki
  • Nomura, Ryosuke
  • Ogihara, Teppei
  • Shimuzu, Yasutaka
  • Uchida, Masayuki
  • Yoshida, Nakahiro

Abstract

The YUIMA Project is an open source and collaborative effort aimed at developing the R package yuima for simulation and inference of stochastic differential equations. In the yuima package stochastic differential equations can be of very abstract type, multidimensional, driven by Wiener process or fractional Brownian motion with general Hurst parameter, with or without jumps specified as Lévy noise. The yuima package is intended to offer the basic infrastructure on which complex models and inference procedures can be built on. This paper explains the design of the yuima package and provides some examples of applications.

Suggested Citation

  • Brouste, Alexandre & Fukasawa, Masaaki & Hino, Hideitsu & Iacus, Stefano & Kamatani, Kengo & Koike, Yuta & Masuda, Hiroki & Nomura, Ryosuke & Ogihara, Teppei & Shimuzu, Yasutaka & Uchida, Masayuki & Y, 2014. "The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i04).
    • Handle: RePEc:jss:jstsof:v:057:i04
    DOI: http://hdl.handle.net/10.18637/jss.v057.i04
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    References listed on IDEAS

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    1. Alexandre Brouste & Stefano Iacus, 2013. "Parameter estimation for the discretely observed fractional Ornstein–Uhlenbeck process and the Yuima R package," Computational Statistics, Springer, vol. 28(4), pages 1529-1547, August.
    2. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
    3. Zeileis, Achim & Grothendieck, Gabor, 2005. "zoo: S3 Infrastructure for Regular and Irregular Time Series," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i06).
    4. T. Ogihara & N. Yoshida, 2011. "Quasi-likelihood analysis for the stochastic differential equation with jumps," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 189-229, October.
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    13. Hiroki Masuda & Yuma Uehara, 2017. "Two-step estimation of ergodic Lévy driven SDE," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 105-137, April.
    14. Tiziana Carpi & Airo Hino & Stefano Maria Iacus & Giuseppe Porro, 2021. "Twitter Subjective Well-Being Indicator During COVID-19 Pandemic: A Cross-Country Comparative Study," Papers 2101.07695, arXiv.org.
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    17. Stefano Iacus & Lorenzo Mercuri, 2015. "Implementation of Lévy CARMA model in Yuima package," Computational Statistics, Springer, vol. 30(4), pages 1111-1141, December.
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    22. Shoichi Eguchi & Hiroki Masuda, 2019. "Data driven time scale in Gaussian quasi-likelihood inference," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 383-430, October.

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