  We use data from a recent long ASCA observation of the Narrow Line Seyfert 1
Ark 564 to investigate in detail its timing properties. We show that a thorough
analysis of the time series, employing techniques not generally applied to AGN
light curves, can provide useful information to characterize the engines of
these powerful sources.We searched for signs of non-stationarity in the data,
but did not find strong evidences for it. We find that the process causing the
variability is very likely nonlinear, suggesting that variability models based
on many active regions, as the shot noise model, may not be applicable to Ark
564. The complex light curve can be viewed, for a limited range of time scales,
as a fractal object with non-trivial fractal dimension and statistical
self-similarity. Finally, using a nonlinear statistic based on the scaling
index as a tool to discriminate time series, we demonstrate that the high and
low count rate states, which are indistinguishable on the basis of their
autocorrelation, structure and probability density functions, are intrinsically
different, with the high state characterized by higher complexity.
