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Agatha is a framework of periodograms to disentangle periodic signals from correlated noise and to solve the two-dimensional model selection problem: signal dimension and noise model dimension. These periodograms are calculated by applying likelihood maximization and marginalization and combined in a self-consistent way. Agatha can be used to select the optimal noise model and to test the consistency of signals in time and can be applied to time series analyses in other astronomical and scientific disciplines. An interactive web implementation of the software is also available at http://agatha.herts.ac.uk/.