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Don't Bleach Chaotic Data

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  • James Theiler
  • Stephen Eubank
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    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.

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    Bibliographic Info

    Paper provided by Santa Fe Institute in its series Working Papers with number 93-05-026.

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    Date of creation: May 1993
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    Handle: RePEc:wop:safiwp:93-05-026

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    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. 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.

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