  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.
