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Quantitative Assessment of the Log-Log-Step Method for Pattern Detection in Noise-Prone Environments

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  • Florian Gomez
  • Ruedi Stoop

Abstract

Staircase-like structures in the log-log correlation plot of a time series indicate patterns against a noisy background, even under condition of strong jitter. We analyze the method for different jitter-noise-combinations, using quantitative criteria to measure the achievement by the method. A phase diagram shows the remarkable potential of this method even under very unfavorable conditions of noise and jitter. Moreover, we provide a novel and compact analytical derivation of the upper and lower bounds on the number of steps observable in the ideal noiseless case, as a function of pattern length and embedding dimension. The quantitative measure developed combined with the ideal bounds can serve as guiding lines for determining potential periodicity in noisy data.

Suggested Citation

  • Florian Gomez & Ruedi Stoop, 2011. "Quantitative Assessment of the Log-Log-Step Method for Pattern Detection in Noise-Prone Environments," PLOS ONE, Public Library of Science, vol. 6(12), pages 1-5, December.
    • Handle: RePEc:plo:pone00:0028107
    DOI: 10.1371/journal.pone.0028107
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