title: Quantitative assessment of the log-log-step method for pattern detection in noise-prone environments.
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.
authors.affiliation: Institute of Neuroinformatics, ETH Zurich and University of Zurich, Zurich, Switzerland.
authors.forename: Florian
authors.initials: F
authors.lastname: Gomez
authors.forename: Ruedi
authors.initials: R
authors.lastname: Stoop
mesh_terms: D000465:Algorithms; D009622:Noise; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results