The hunt for Earth analogue planets orbiting Sun-like stars has forced the introduction of novel methods to detect signals at, or below, the level of the intrinsic noise of the observations. We present a new global periodogram method that returns more information than the classic Lomb-Scargle periodogram method for radial velocity signal detection. Our method uses the Minimum Mean Squared Error as a framework to determine the optimal number of genuine signals present in a radial velocity timeseries using a global search algorithm, meaning we can discard noise spikes from the data before follow-up analysis. This method also allows us to determine the phase and amplitude of the signals we detect, meaning we can track these quantities as a function of time to test if the signals are stationary or non-stationary. We apply our method to the radial velocity data for GJ876 as a test system to highlight how the phase information can be used to select against non-stationary sources of detected signals in radial velocity data, such as rotational modulation of star spots. Analysis of this system yields two new statistically significant signals in the combined Keck and HARPS velocities with periods of 10 and 15 days. Although a planet with a period of 15 days would relate to a Laplace resonant chain configuration with three of the other planets (8:4:2:1), we stress that follow-up dynamical analyses are needed to test the reliability of such a six planet system.
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