  We study the X-ray variability properties of distant AGNs in the Chandra Deep
Field-South region over 17 years, up to $z\sim 4$, and compare them with those
predicted by models based on local samples. We use the results of Monte Carlo
simulations to account for the biases introduced by the discontinuous sampling
and the low-count regime. We confirm that variability is an ubiquitous property
of AGNs, with no clear dependence on the density of the environment. The
variability properties of high-z AGNs, over different temporal timescales, are
most consistent with a Power Spectral Density (PSD) described by a broken (or
bending) power-law, similar to nearby AGNs. We confirm the presence of an
anti-correlation between luminosity and variability, resulting from the
dependence of variability on BH mass and accretion rate. We explore different
models, finding that our acceptable solutions predict that BH mass influences
the value of the PSD break frequency, while the Eddington ratio $\lambda_{Edd}$
affects the PSD break frequency and, possibly, the PSD amplitude as well. We
derive the evolution of the average $\lambda_{Edd}$ as a function of redshift,
finding results in agreement with measurements based on different estimators.
The large statistical uncertainties make our results consistent with a constant
Eddington ratio, although one of our models suggest a possible increase of
$\lambda_{Edd}$ with lookback time up to $z\sim 2-3$. We conclude that
variability is a viable mean to trace the accretion history of supermassive
BHs, whose usefulness will increase with future, wide-field/large effective
area X-ray missions.
