  As the hunt for an Earth-like exoplanets has intensified in recent years, so
has the effort to characterise and model the stellar signals that can hide or
mimic small planetary signals. Stellar variability arises from a number of
sources, including granulation, supergranulation, oscillations and activity,
all of which result in quasi-periodic or stochastic behaviour in photometric
and/or radial velocity observations. Traditionally, the characterisation of
these signals has mostly been done in the frequency domain. However, the recent
development of scalable Gaussian process regression methods makes direct
time-domain modelling of stochastic processes a feasible and arguably
preferable alternative, obviating the need to estimate the power spectral
density of the data before modelling it. In this paper, we compare the two
approaches using a series of experiments on simulated data. We show that
frequency domain modelling can lead to inaccurate results, especially when the
time sampling is irregular. By contrast, Gaussian process regression results
are often more precise, and systematically more accurate, in both the regular
and irregular time sampling regimes. While this work was motivated by the
analysis of radial velocity and photometry observations of main sequence stars
in the context of planet searches, we note that our results may also have
applications for the study of other types of astrophysical variability such as
quasi-periodic oscillations in X-ray binaries and active galactic nuclei
variability.
