The impact of background noise on the determination of the fractal and statistical properties of cosmic ray time series

This paper investigates the influence of background white noise on the determination of the colored random noise properties of cosmic ray experimental signals. We consider fractal methods (Grassberger and Procaccia method, scaling exponent method and fractal length method) and statistical methods (comparison with the Gaussian and Rice curves, and the multivariate scaling analysis technique). The investigation is carried out using two experimental time series with different color (spectral indices α = 1.6 and α = 1.2) and, as a reference, several computer simulations of pure noise-free colored random noise signals with 0 ≤ α ≤ 3 with the same number of points. The results of the investigation is that the presence of noise in a experimental signal "deceives" the algorithms employed in the various analyses causing them to sample noiselike properties (e.g., an infinite or very large fractal dimension and Gaussian or quasi-Gaussian behavior), irrespective of the physical characteristics of the particular data set.