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Singular spectrum analysis for astronomical time series: Constructing a parsimonious hypothesis test

  • Author(s): Greco, G
  • Kondrashov, D
  • Kobayashi, S
  • Ghil, M
  • Branchesi, M
  • Guidorzi, C
  • Stratta, G
  • Ciszak, M
  • Marino, F
  • Ortolan, A
  • et al.
Abstract

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/fβ 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.

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