A new approach to the variability characterization of active galactic
  nuclei
  The normalized excess variance is a popular method used by many authors to
estimate the variability of active galactic nuclei (AGNs), especially in the
X-ray band. We show that this estimator is affected by the cosmological time
dilation, so that it should be appropriately corrected when applied to AGN
samples distributed in wide redshift intervals. We propose a formula to modify
this estimator, based on the use of the structure function. To verify the
presence of the cosmological effect and the reliability of the proposed
correction, we use data extracted from the XMM-Newton Serendipitous Source
Catalogue, data release 5 (XMMSSC-DR5), and cross-matched with the Sloan
Digital Sky Survey quasar catalogue, of data release 7 and 12.
