  We present the analysis of the X-ray variability and spectral timing
properties of the ultraluminous X-ray source (ULX) NGC 5408 X-1, one of the
most variable ULXs known so far. The variability properties are used as a
diagnostic of the accretion state of the source and to derive estimates of the
black hole (BH) mass. The observed high level of fast X-ray variability
(fractional root-mean-square variability - rms - amplitude of $\sim$ 30 percent
in the hard energy band), the hardening of the fractional rms spectrum, and the
properties of the QPO, all resemble those of a source in a hard-intermediate
accretion state. We confirm the previous detection of a soft lag in the X-ray
light curves of the source during 2006 and 2008 observations and find that the
soft lag is still present in the more recent 2010/2011 observations. Using the
entire available XMM-Newton data set (public as of February 2012) we observe
that the soft lag (of few seconds amplitude) is detected over a relatively
large range of frequencies ($\nu \sim 5-90$ mHz), which always includes the QPO
frequencies. The soft lag displays energy-dependence, with the (absolute)
amplitude increasing as a function of energy separation. We find close
analogies with soft lags associated to type-C QPOs in BH binary systems
(although an association to other types of QPOs cannot be completely excluded),
as well as with reverberation lags observed in AGN. In both cases an
intermediate mass BH (IMBH) solution appears the most plausible.
