  In photometry, the short-timescale stellar variability ("flicker"), such as
that caused by granulation and oscillations, can reach amplitudes comparable to
the transit depth of Earth-sized planets and is correlated over the typical
transit timescales. It can introduce systematic errors on the inferred
planetary parameters when a small number of transits are observed. The
objective of this paper is to characterize the statistical properties of this
noise and quantify its impact on the inferred transit parameters. We used the
extensive solar observations obtained with SoHO/VIRGO to characterize flicker
noise. We simulated realistic transits across the solar disk using SDO/HMI data
and used these to obtain transit light curves, which we used to estimate the
errors made on the transit parameters. We make these light curves publicly
available. To extend the study to a wider parameter range, we derived the
properties of flicker noise using Kepler observations and studied their
dependence on stellar parameters. Finally, we predicted the limiting stellar
apparent magnitude for which the properties of the flicker noise can be
extracted using high-precision CHEOPS and PLATO observations. Stellar
granulation is a stochastic colored noise, and is stationary with respect to
the stellar magnetic cycle. Both the flicker correlation timescales and
amplitudes increase with the stellar mass and radius. If these correlations are
not taken into account when fitting for the parameters of transiting
exoplanets, this can bias the inferred parameters. In particular, we find
errors of up to 10$\%$ on $R_p/R_s$ for an Earth-sized planet orbiting a
Sun-like star. For F and G stars, flicker will significantly affect the
inferred parameters of transits observed with CHEOPS and PLATO. Dedicated
modeling strategies need to be developed to accurately characterize both the
star and the transiting exoplanets.
