Wavelet analysis: a new significance test for signals dominated by intrinsic red-noise variability

TL;DR

This paper introduces a new statistical test for wavelet power spectra to detect significant quasi-periodic oscillations in signals with red-noise variability, especially useful for astronomical X-ray light curves.

Contribution

The authors develop a novel significance test for wavelet analysis tailored to signals with red-noise, applicable to X-ray astronomy and other 1/f^alpha variability signals.

Findings

Successfully detected QPOs in XTE J1550--564 and RE J1034+396

Validated the method's effectiveness in wavelet domain analysis

Demonstrated applicability to general red-noise dominated signals

Abstract

We develop a new statistical test for the wavelet power spectrum. We design it with purpose of testing signals which intrinsic variability displays in a Fourier domain a red-noise component described by a single, broken or doubly-broken power-law model. We formulate our methodology as straightforwardly applicable to astronomical X-ray light curves and aimed at judging the significance level for detected quasi-periodic oscillations (QPOs). Our test is based on a comparison of wavelet coefficients derived for the source signal with these obtained from the averaged wavelet decomposition of simulated signal which preserves the same broad-band model of variability as displayed by X-ray source. We perform a test for statistically significant QPO detection in XTE J1550--564 microquasar and active galaxy of RE J1034+396 confirming these results in the wavelet domain with our method. In addition, we argue on the usefulness of our new algorithm for general class of signals displaying 1/f^alpha-type variability.