Generalized Lomb-Scargle periodograms of the de-trended time series data and of the residuals after correcting for the 16.3-day signal with a simple sinusoidal fit. In panels a and b this is shown for the radial velocities, in panels c and d for the S index, and in panels e and f for the Hα index. Additionally, we show in panel g the window function of the time series. Yellow lines indicate the important periodic signals for GJ 3942, namely 16.3, 10.4, and 6.9 days, and we also show additional periodicities mentioned in the text. The dashed blue horizontal line shows the 1% FAP level of the respective dataset.