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Periodograms are used as a key significance assessment and visualisation toolto display the significant periodicities in unevenly sampled time series. Weintroduce a framework of periodograms, called "Agatha", to disentangle periodicsignals from correlated noise and to solve the 2-dimensional model selectionproblem: signal dimension and noise model dimension. These periodograms arecalculated by applying likelihood maximization and marginalization and combinedin a self-consistent way. We compare Agatha with other periodograms for thedetection of Keplerian signals in synthetic radial velocity data produced forthe Radial Velocity Challenge as well as in radial velocity datasets of severalSun-like stars. In our tests we find Agatha is able to recover signals to theadopted detection limit of the radial velocity challenge. Applied to realradial velocity, we use Agatha to confirm previous analysis of CoRoT-7 and tofind two new planet candidates with minimum masses of 15.1 $M_\oplus$ and 7.08$M_\oplus$ orbiting HD177565 and HD41248, with periods of 44.5 d and 13.4 d,respectively. We find that Agatha outperforms other periodograms in terms ofremoving correlated noise and assessing the significances of signals with morerobust metrics. Moreover, it can be used to select the optimal noise model andto test the consistency of signals in time. Agatha is intended to be flexibleenough to be applied to time series analyses in other astronomical andscientific disciplines. Agatha is available at http://www.agatha.herts.ac.uk.

Agatha: disentangling periodic signals from correlated noise in a periodogram framework