Top panel: O–C residuals for HATS-2b in the case (a), superimposed with the best-fitting linear ephemeris model (black line), the best-fitting quadratic ephemeris model (red line) and the best-fitting cosinusoidal ephemeris model (cyan line). The purple points represent the times derived from the Danish 1.54 m telescope observations, the yellow points the times derived from the MPG/ESO 2.2 m telescope data, and the blue points the times derived from TESS data. Bottom panel: same as the top panel but for case (b), i.e. also considering the data from the ExoClock database, which are represented as green points.