We present calculations of the time lags and the coherence function of
X-ray photons for a novel model of radiation emission from accretion-
powered high-energy sources. Our model involves only Comptonization of
soft photons injected near the compact object in an extended but nonu
niform atmosphere around the compact object. Our results show that thi
s model produces time lags between the hard and soft bands of the X-ra
y spectrum that increase with Fourier period, in agreement with recent
Observations; it also produces a coherence function equal to one over
a wide range of frequencies if the system parameters do not change si
gnificantly during the observation, also in agreement with the limited
existing observations. We explore various conditions that could affec
t coherence functions. We indicate that measurements of these statisti
cal quantities could provide diagnostics of the radial variation of th
e density of this class of sources.