Singular Spectrum Analysis for Astronomical Time Series: Constructing a Parsimonious Hypothesis Test
Authors: Greco G., Kondrashov D., Kobayashi S., Ghil M., Branchesi M., Guidorzi C., Stratta G., Ciszak M., Marino F., Ortolan A.
Autors Affiliation: Università degli Studi di Urbino “Carlo Bo” – DiSBeF, Urbino, PU I-61029, Italy; INFN, Sezione di Firenze, Via Sansone 1, Sesto Fiorentino, FI I-50019, Italy; University of California – AOS and IGPP, Los Angeles, CA 90095-1565, United States; Ecole Normale Supérieure – CNRS and IPSL, Paris Cedex 05, F-75231, France; ARI – Liverpool John Moores University, 146 Brownlow Hill, Liverpool, L3 5RF, United Kingdom; Department of Physics and Earth Sciences, University of Ferrara, Ferrara, I-44122, Italy; CNR-Istituto Nazionale di Ottica, L.go E. Fermi 6, Firenze, I-50125, Italy; INFN, Laboratori Nazionali di Legnaro, Legnaro, PD I-35020, Italy
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/f ß 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.
Conference title: A Meeting to Honour the 70th Birthday of Massimo Capaccioli
More Information: 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).KeyWords: Extrasolar planets; Monte Carlo methods; Spectrum analysis; Stochastic systems; Surveys, Coherent phenomena; First order autoregressive; Hypothesis tests; Monte-Carlo Singular Spectrum Analysis; Power-law noise; Singular spectrum analysis; Spectral methods; Stochastic variation, Time series analysis