Singular Spectrum Analysis for astronomical time series: constructing a parsimonious hypothesis test

TL;DR

This paper introduces Monte Carlo Singular Spectrum Analysis (MC-SSA), a spectral method designed to analyze astrophysical time series with complex noise, effectively distinguishing signals from noise even at low signal levels.

Contribution

The paper develops a novel, data-adaptive spectral analysis method, MC-SSA, tailored for astrophysical data contaminated with $1/f^{eta}$ noise and Poisson noise, demonstrating its robustness and broad applicability.

Findings

MC-SSA effectively handles $1/f^{eta}$ noise in astrophysical data.

The method remains effective even when signals are below detection thresholds.

MC-SSA can be applied to various astrophysical problems, including exoplanet detection and transient phenomena.

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 $1/f^{\beta}$ 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.