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Red Noise–based False Alarm Thresholds for Astrophysical Periodograms via Whittle’s Approximation to the Likelihood

  • Authors: Amna Ejaz, Sarah Dodson-Robinson, Charlotte Haley

Amna Ejaz et al 2026 The Astronomical Journal 171 .

  • Provider: AAS Journals

Caption: Figure 15.

Panel (a): time-domain realization of an AR(1) process with ϕ = 0.77 and σw = 1.0. Panel (b): periodogram ﹩{\hat{S}}^{LS}(f)﹩ (light blue) and true power spectrum S(f) (dark blue) of the time series in panel (a). Panel (c): whitened log-periodogram ﹩{\rm{log}}\left[{\hat{S}}^{{\rm{LS}}}(f)\right]-{\rm{log}}\left[S(f)\right]﹩ overlaid with 1% and 5% ﹩{\chi }_{2}^{2}﹩ quantiles (orange and green solid lines, respectively) and 1% and 5% whitened Monte Carlo FALs (orange and green dotted lines).

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