  We present a data-adaptive spectral method - Monte Carlo Singular Spectrum
Analysis (MC-SSA) - and its modification to tackle astrophysical problems.
Through numerical simulations we show the ability of the MC-SSA in dealing with
$1/f^{\beta}$ power-law noise affected by photon counting statistics. Such
noise process is simulated by a first-order autoregressive, AR(1) process
corrupted by intrinsic Poisson noise. In doing so, we statistically estimate a
basic stochastic variation of the source and the corresponding fluctuations due
to the quantum nature of light. In addition, MC-SSA test retains its
effectiveness even when a significant percentage of the signal falls below a
certain level of detection, e.g., caused by the instrument sensitivity. The
parsimonious approach presented here may be broadly applied, from the search
for extrasolar planets to the extraction of low-intensity coherent phenomena
probably hidden in high energy transients.
