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Computing the multifractal spectrum from time series: an algorithmic approach.

K P Harikrishnan1, R Misra, G Ambika

  • 1Department of Physics, The Cochin College, Cochin 682 002, India.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

This study introduces an improved algorithmic scheme for computing the f(alpha) spectrum from time series data. The new method accurately calculates the complete spectrum, including for noisy real-world systems.

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Area of Science:

  • Nonlinear dynamics
  • Time series analysis
  • Fractal analysis

Background:

  • Existing methods for computing the f(alpha) spectrum from time series data often yield incomplete results.
  • These standard schemes typically compute only the upper portion of the f(alpha) spectrum.

Purpose of the Study:

  • To develop and validate a novel algorithmic scheme for enhanced f(alpha) spectrum computation from time series.
  • To enable the computation of complete D(q) and f(alpha) spectra for any embedding dimension.
  • To adapt the scheme for analyzing practical, noisy time series.

Main Methods:

  • The new scheme fits the f(alpha) spectrum profile with an analytic function of four independent parameters.
  • Algorithmic automation is employed to compute D(q) and f(alpha) spectra.
  • The method is tested on the logistic attractor and applied to higher-dimensional and noisy real-world time series.

Main Results:

  • The proposed scheme successfully computes complete f(alpha) and D(q) spectra, overcoming limitations of existing methods.
  • The algorithm effectively handles time series with noise and is applicable to higher embedding dimensions.
  • Preliminary findings suggest the four parameters can serve as diagnostic measures.

Conclusions:

  • The new algorithmic scheme offers a significant improvement for computing f(alpha) spectra from time series.
  • This method provides a robust tool for analyzing complex and noisy dynamical systems.
  • The identified parameters hold potential for system diagnostics in time series analysis.