Singular Spectrum Analysis for Astronomical Time Series: Constructing a Parsimonious Hypothesis Test
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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 β 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.
KeywordsColored Noise Singular Spectrum Analysis Poisson Noise Extrasolar Planet Astrophysical Application
MB, GG and GS acknowledge the financial support of the Italian Ministry of Education, University and Research (MIUR) through grant FIRB 2012 RBFR12PM1F. CG acknowledges the PRIN MIUR project on “Gamma Ray Bursts: from progenitors to physics of the prompt emission process” (Prot. 2009 ERC3HT). MG and DK received support from the U.S. National Science Foundation (grant DMS-1049253) and from the U.S. Office of Naval Research (MURI grant N00014-12-1-0911).