IDEAS home Printed from https://ideas.repec.org/a/bpj/sndecm/v1y1996i3n2.html
   My bibliography  Save this article

The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms

Author

Listed:
  • Gencay Ramazan

    (Department of Economics, Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, Canada, gencay@uwin)

  • Dechert W. Davis

    (Department of Economics, University of Houston, Houston, Texas, USA)

Abstract

The method of reconstructing an n-dimensional system from observations is to form vectors of m consecutive observations, which for m 2n, is generically an embedding. This is Takens's result. The Jacobian methods for Lyapunov exponents utilize a function of m variables to model the data, and the Jacobian matrix is constructed at each point in the orbit of the data. When embedding occurs at dimension m = n, the Lyapunov exponents of the reconstructed dynamics are the Lyapunov exponents of the original dynamics. However, if embedding only occurs for an m > n, then the Jacobian method yields m Lyapunov exponents, only n of which are the Lyapunov exponents of the original system. The problem is that as currently used, the Jacobian method is applied to the full m-dimensional space of the reconstruction, and not just to the n-dimensional manifold that is the image of the embedding map. Our examples show that it is possible to obtain spurious Lyapunov exponents that are even larger than the largest Lyapunov exponent of the original system.

Suggested Citation

  • Gencay Ramazan & Dechert W. Davis, 1996. "The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(3), pages 1-12, October.
    • Handle: RePEc:bpj:sndecm:v:1:y:1996:i:3:n:2
    DOI: 10.2202/1558-3708.1018
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1558-3708.1018
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1558-3708.1018?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    2. Simón Sosvilla-Rivero & Fernando Fernández-Rodriguez & Julián Andrada-Félix, 2005. "Testing chaotic dynamics via Lyapunov exponents," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 911-930.
    3. repec:zbw:bofrdp:2007_020 is not listed on IDEAS
    4. Bask, Mikael & Liu, Tung & Widerberg, Anna, 2007. "The stability of electricity prices: Estimation and inference of the Lyapunov exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 565-572.
    5. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    6. Bask, Mikael & Widerberg, Anna, 2009. "Market structure and the stability and volatility of electricity prices," Energy Economics, Elsevier, vol. 31(2), pages 278-288, March.
    7. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    8. Anagnostidis, Panagiotis & Emmanouilides, Christos J., 2015. "Nonlinearity in high-frequency stock returns: Evidence from the Athens Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 473-487.
    9. Maus, A. & Sprott, J.C., 2013. "Evaluating Lyapunov exponent spectra with neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 13-21.

    More about this item

    Keywords

    Lyapunov exponents; embedded dynamics;

    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:bpj:sndecm:v:1:y:1996:i:3:n:2. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.