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Mathematics - Physics

Quantitative Assessment of the Log-Log-Step Method for Pattern Detection in Noise-Prone Environments
Published: Monday, December 12, 2011
Author: Florian Gomez et al.

by Florian Gomez, Ruedi Stoop

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.