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

Florian Gomez and Ruedi Stoop

PLOS ONE, 2011, vol. 6, issue 12, 1-5

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0028107

DOI: 10.1371/journal.pone.0028107

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