Illustration of the reliability of different FAP estimates of test T_M depending on the noise characteristics under and on the technique involved. Top: FAP as a function of the detection threshold γ in the case where the data under is a WGN of standard deviation σ = 49 cm s⁻¹ (first column) or the colored solar time series of same variance (last two columns). Panel a: the blue curve corresponds to the FAP of test T_M with known variance σ² (see Eq. (20)). The red curve corresponds to the FAP of test estimated by bootstrap using one estimate of the variance from one time series, . The dark green curve represents the true FAP of . The curves in orange show 100 FAP estimates of the same test but obtained for 100 different estimates of . Panel b: the red curve shows the FAP of test , evaluated by bootstrap on one GOLF solar time series with estimated variance . The dark green curve shows the true FAP of this test, as estimated using the N_series− 1 other GOLF time series. The orange (resp. light green) curves are the same as the red (resp. the dark green) curves, but using each time a different GOLF time series as input. Panel c: the green curve represents the analytic FAP of T_M based on the simulation-standardized periodogram with L = 20 MHD time series (see Eq.(13)) and the red curve represents the true FAP estimated using N_series = 1640 GOLF time series. Bottom: empirical distribution of test statistics T_M as estimated by bootstrap (panels d and e) and by MC simulations of the GOLF series standardized by the MHD simulations (panel f). In all six panels, the thresholds inferred for FAPs of 1 and 10% by each technique are indicated by the dashed and dotted lines, respectively. The color used for the thresholds in each bottom panel corresponds to the color used for each method in the corresponding upper panel. Numerical values are indicated in Table. 1.