Article describes how detrended fluctuation analysis (DFA) is a well-established method to evaluate scaling indices of time series, which categorize the dynamics of complex systems. The authors propose treating each reaction time as a duration time that changes the representation from operational (trial number) time n to event (temporal) time t, or X(t).

Authors of the article explain that they investigated the extreme X-ray variability of a z = 1.608 active galactic nucleus in the 7 Ms Chandra Deep Field-South (XID 403), which showed two significant X-ray brightening events.

Authors of the article assert that they studied the ensemble X-ray variability properties of active galactic nuclei (AGN) over large ranges of timescale (20 ks ≤ T ≤ 14 yr), redshift (0 ≤ z ≲ 3), luminosity (1040 erg s−1 ≤ LX ≤ 1046 erg s−1), and black hole (BH) mass (106 ≤ M⊙ ≤ 109). The authors show that the data collected from archival observations and previous literature studies are fully consistent with a universal PSD form, which does not show any evidence for systematic evolution of shape or amplitude with redshift or luminosity, even if there may be differences between individual AGN at a given redshift or luminosity.