CARMENES data. Left: Time series for the S-BART RVs and the spectroscopic activity indicators. The grey line shows a quadratic trend fit. Center: Activity indicator and RV correlation, with a linear fit shown in dashed blue line, and the correlation coefficients (R from Pearson, and ρ from Spearman) indicated in the grey box. Right: GLS periodogram to the time series of the same row. The grey line corresponds to the non-detrended time series, while colored lines correspond to the same dataset after subtracting the fitted quadratic function. Vertical lines indicate the periodicities of the planets (blue and green), the rotational period (red region, see Sect. 3.2) and its half (dashed red line), and the duration of the year and its half (dashed grey lines). Horizontal lines show different false alarm probabilities as indicated in the top panel.