Quantitative assessment of the log-log-step method for pattern detection in noise-prone environments

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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. © 2011 Gomez, Stoop.

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Gomez, F., & Stoop, R. (2011). Quantitative assessment of the log-log-step method for pattern detection in noise-prone environments. PLoS ONE, 6(12). https://doi.org/10.1371/journal.pone.0028107

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