IDEAS home Printed from https://ideas.repec.org/p/wop/safiwp/93-05-026.html
   My bibliography  Save this paper

Don't Bleach Chaotic Data

Author

Listed:
  • James Theiler
  • Stephen Eubank

Abstract

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ``bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.

Suggested Citation

  • James Theiler & Stephen Eubank, 1993. "Don't Bleach Chaotic Data," Working Papers 93-05-026, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:93-05-026
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Antonios Antoniou & Constantinos E. Vorlow, 2004. "Price Clustering and Discreteness: Is there Chaos behind the Noise?," Papers cond-mat/0407471, arXiv.org.
    2. Small Michael & Tse Chi K., 2003. "Determinism in Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(3), pages 1-31, October.
    3. Nakamura, Tomomichi & Small, Michael, 2006. "Testing for dynamics in the irregular fluctuations of financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 377-386.
    4. Antoniou, Antonios & Vorlow, Constantinos E., 2005. "Price clustering and discreteness: is there chaos behind the noise?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 389-403.
    5. Marcos Álvarez-Díaz & Rangan Gupta, 2015. "Forecasting the US CPI: Does Nonlinearity Matter?," Working Papers 201512, University of Pretoria, Department of Economics.
    6. Karagianni Stella & Kyrtsou Catherine, 2011. "Analysing the Dynamics between U.S. Inflation and Dow Jones Index Using Non-Linear Methods," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-25, March.
    7. Álvarez-Díaz, Marcos & Hammoudeh, Shawkat & Gupta, Rangan, 2014. "Detecting predictable non-linear dynamics in Dow Jones Islamic Market and Dow Jones Industrial Average indices using nonparametric regressions," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 22-35.
    8. Kyrtsou, Catherine, 2008. "Re-examining the sources of heteroskedasticity: The paradigm of noisy chaotic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6785-6789.

    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:wop:safiwp:93-05-026. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel). General contact details of provider: http://edirc.repec.org/data/epstfus.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.