  X-ray variability of accreting black hole binaries is believed to be produced
by the fluctuations propagating towards the compact object. Observations
suggest the light curves in different energy bands are connected, but the
fluctuations at harder energies are delayed with respect to the softer ones.
The standard interpretation involves dependence of the X-ray spectral hardness
on the radial distance, with harder spectra emitted closer to the black hole.
Recently, a number of challenges to this scenario have been found, both at
qualitative and quantitative level. The model does not predict the large
magnitude of the delay between different energies, as well as the dependence of
variability amplitude on the spectral range and frequency. We study timing
properties of accreting black hole X-ray binaries taking into account
peculiarities of spectral formation in these sources. We show that the
simultaneous presence of two components leads to a complex shape of power
spectra and phase lags between the X-ray bands: the amplitude of the phase lag
becomes independent of the delay between the components, and the power spectra
show an artificial decrease or, on the contrary, enhancement of power at low
Fourier frequencies. This provides an essential ingredient for the
reinstatement of the propagating fluctuations model. The work draws attention
to the importance of considering conditions of spectral formation when studying
timing properties.
