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Searches for periodicity in time series are often done with models ofperiodic signals, whose statistical significance is assessed via false alarmprobabilities or Bayes factors. However, a statistically significant periodicmodel might not originate from a strictly periodic source. In astronomy inparticular, one expects transient signals that show periodicity for a certainamount of time before vanishing. This situation is encountered for instance inthe search for planets in radial velocity data. While planetary signals areexpected to have a stable phase, amplitude and frequency - except when strongplanet-planet interactions are present - signals induced by stellar activitywill typically not exhibit the same stability. In the present article, weexplore the use of periodic functions multiplied by time windows to diagnosewhether an apparently periodic signal is truly so. We suggest diagnostics tocheck whether a signal is consistently present in the time series, and has astable phase, amplitude and period. The tests are expressed both in aperiodogram and Bayesian framework. Our methods are applied to the SolarHARPS-N data as well as HD 215152, HD 69830 and HD 13808. We find that (i) theHARPS-N Solar data exhibits signals at the Solar rotation period and its firstharmonic ($\sim$ 13.4 days). The frequency and phase of the 13.4 days signalappear constant within the estimation uncertainties, but its amplitude presentssignificant variations which can be mapped to activity levels. (ii) aspreviously reported, we find four, three and two planets orbiting HD 215152, HD69830 and HD 13808.

Testing whether a signal is strictly periodic. Application to disentangling planets and stellar activity in radial velocities