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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.

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