  In recent years, Gaussian Process (GP) regression has become widely used to
analyse stellar and exoplanet time-series data sets. For spotted stars, the
most popular GP covariance function is the quasi-periodic (QP) kernel, whose
the hyperparameters of the GP have a plausible interpretation in terms of
physical properties of the star and spots. In this paper, we test the
reliability of this interpretation by modelling data simulated using a spot
model using a QP GP, and the recently proposed quasi-periodic plus cosine (QPC)
GP, comparing the posterior distributions of the GP hyperparameters to the
input parameters of the spot model. We find excellent agreement between the
input stellar rotation period and the QP and QPC GP period, and very good
agreement between the spot decay timescale and the length scale of the squared
exponential term. We also compare the hyperparameters derived from light and
radial velocity (RV) curves for a given star, finding that the period and
evolution timescales are in good agreement. However, the harmonic complexity of
the GP, while displaying no clear correlation with the spot properties in our
simulations, is systematically higher for the RV than for the light curve data.
Finally, for the QP kernel, we investigate the impact of noise and
time-sampling on the hyperparameters in the case of RVs. Our results indicate
that good coverage of rotation period and spot evolution time-scales is more
important than the total number of points, and noise characteristics govern the
harmonic complexity.
