IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v98y2025i2d10.1140_epjb_s10051-025-00883-9.html
   My bibliography  Save this article

Local statistical moments to capture Kramers–Moyal coefficients

Author

Listed:
  • Christian Wiedemann

    (Carl von Ossietzky Universität Oldenburg
    ForWind, Center for Wind Energy Research
    Carl von Ossietzky Universität Oldenburg)

  • Matthias Wächter

    (Carl von Ossietzky Universität Oldenburg
    ForWind, Center for Wind Energy Research)

  • Jan A. Freund

    (Carl von Ossietzky Universität Oldenburg
    Carl von Ossietzky Universität Oldenburg)

  • Joachim Peinke

    (Carl von Ossietzky Universität Oldenburg
    ForWind, Center for Wind Energy Research)

Abstract

This study introduces an innovative local statistical moment approach for estimating Kramers–Moyal coefficients, effectively bridging the gap between nonparametric and parametric methodologies. These coefficients play a crucial role in characterizing stochastic processes. Our proposed approach provides a versatile framework for localized coefficient estimation, combining the flexibility of nonparametric methods with the interpretability of global parametric approaches. We showcase the efficacy of our approach through use cases involving both stationary and non-stationary time series analysis. Additionally, we demonstrate its applicability to real-world complex systems, specifically in the energy conversion process analysis of a wind turbine. Graphic abstract

Suggested Citation

  • Christian Wiedemann & Matthias Wächter & Jan A. Freund & Joachim Peinke, 2025. "Local statistical moments to capture Kramers–Moyal coefficients," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(2), pages 1-13, February.
    • Handle: RePEc:spr:eurphb:v:98:y:2025:i:2:d:10.1140_epjb_s10051-025-00883-9
    DOI: 10.1140/epjb/s10051-025-00883-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1140/epjb/s10051-025-00883-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1140/epjb/s10051-025-00883-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Clemens Willers & Oliver Kamps, 2021. "Non-parametric estimation of a Langevin model driven by correlated noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(7), pages 1-15, July.
    2. D. Kleinhans & R. Friedrich, 2006. "Maximum Likelihood Estimation of Drift and Diffusion Functions," Papers physics/0611102, arXiv.org, revised Mar 2007.
    3. Christian Wiedemann & Matthias Wächter & Joachim Peinke & Jan A. Freund, 2024. "Improved estimation of drift coefficients using optimal local bandwidths," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(4), pages 1-10, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Varughese, Melvin M., 2013. "Parameter estimation for multivariate diffusion systems," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 417-428.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:eurphb:v:98:y:2025:i:2:d:10.1140_epjb_s10051-025-00883-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.