Radial-velocity data analysis. Left panels: HIRES radial velocities of HAT-P-11 (black circles) showing a clear long-term trend likely due to the stellar magnetic activity cycle. The best-fit models including both the Keplerian signal of HAT-P-11 b and Gaussian-process regression with squared-exponential (top; Eq. (3)), quasi-periodic (middle; Eq. (4)), and quasi-periodic+squared-exponential (bottom; Eq. (5)) kernels are indicated with red solid lines. Right panels: HAT-P-11 RVs (black circles) phase-folded with the transit ephemeris of HAT-P-11 b, after removing the long-term trends modelled with Gaussian processes and the same kernels as in the corresponding left panels. The Keplerian eccentric model is displayed with a red solid line. We note the smaller and smaller scatter in the residuals as we move from top (SE kernel) to bottom (QP+SE kernel).