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Related Experiment Videos

Don't bleach chaotic data.

James Theiler1, Stephen Eubank

  • 1Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545;Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, New Mexico 87501Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, New Mexico 87501Prediction Company, 320 Aztec Street, Santa Fe, New Mexico 87501.

Chaos (Woodbury, N.Y.)
|October 1, 1993
PubMed
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Digital filtering "bleaches" time series data, removing linear correlations. However, this process can obscure the nonlinear dynamics of chaotic systems, leading to inaccurate analysis of chaotic signals.

Area of Science:

  • Signal Processing
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • Time series analysis commonly uses digital filtering to remove linear correlations.
  • This process, known as "bleaching," aims to produce spectrally white residual data.
  • Linear autocorrelation can yield spurious results in nonlinear invariant estimation (e.g., fractal dimension, Lyapunov exponents).

Purpose of the Study:

  • To investigate the practical impact of data bleaching on the analysis of nonlinear time series.
  • To determine if bleaching, theoretically beneficial, hinders the analysis of chaotic processes.
  • To demonstrate the adverse effects of bleaching on chaotic data through numerical experiments.

Main Methods:

  • Application of digital filtering techniques to generate spectrally white time series data.

Related Experiment Videos

  • Numerical experiments using known chaotic time series datasets.
  • Comparison of nonlinear invariant estimation before and after data bleaching.

    • Main Results:

    • Bleaching successfully removes linear correlations, resulting in spectrally white data.
    • In practice, data bleaching obscures the underlying deterministic structure of low-dimensional chaotic processes.
    • Nonchaotic data are not similarly affected by the bleaching process.
    • Adverse effects of bleaching were demonstrated on chaotic data.

    Conclusions:

    • While theoretically sound for removing linear artifacts, data bleaching can obscure essential nonlinear dynamics in chaotic systems.
    • The "bleaching" of time series data is problematic for analyzing chaotic processes.
    • This effect appears intrinsic to the nature of chaos itself.