Crossover scaling evaluation in mixed correlated signals by means of Detrended Fluctuation Analysis

In this work we study the scaling behavior of signals constructed by a class of processes with "intrinsic trends" and correlated noises. We focus our attention in evaluating the appearence of a crossover in the scaling exponents obtained by means of the Detrended Fluctuation Analysis. In particular, we evaluate the conditions of the trend which leads to a crossover where the scaling exponent from small scales (alpha(s)) is smaller or larger than the corresponding exponent from large scales (alpha(l)). We find that decreasing trend leads to alpha(s) > alpha(l), whereas an increasing trend results in alpha(s) < alpha(l). We also find that when one introduces correlated noise into a decreasing or increasing trend map, there is a crossover which separates two regions with exponents related to the trend mainly over short scales for decreasing trends, while over large scales, the scaling exponent resembles the behavior of the increasing trend.