  Kepler-30 is a unique target to study stellar activity and rotation in a
young solar-like star accompanied by a compact planetary system. We use about 4
years of high-precision photometry collected by the Kepler mission to
investigate the fluctuations caused by photospheric convection, stellar
rotation, and starspot evolution as a function of the timescale. Our main goal
is to apply methods for the analysis of timeseries to find the timescales of
the phenomena that affect the light variations. We correlate those timescales
with periodicities in the star as well as in the planetary system. We model the
flux rotational modulation induced by active regions using spot modelling and
apply the MFDMA in standard and multiscale versions for analysing the behaviour
of variability and light fluctuations that can be associated with stellar
convection and the evolution of magnetic fields on timescales ranging from less
than 1 day up to about 35 days. The light fluctuations produced by stellar
activity can be described by the multifractal Hurst index that provides a
measure of their persistence. The spot modeling indicates a lower limit to the
relative surface differential rotation of $\Delta \Omega/\Omega\sim 0.02\pm
0.01$ and suggests a short-term cyclic variation in the starspot area with a
period of $\sim 34$ days, virtually close to the synodic period of 35.2 days of
the planet Kepler-30b. By subtracting the two timeseries of the SAP and PDC
Kepler pipelines, we reduce the rotational modulation and find a 23.1-day
period close to the synodic period of Kepler-30c. This period also appears in
the multifractal analysis as a crossover of the fluctuation functions
associated with the characteristic evolutionary timescales of the active
regions in Kepler-30 as confirmed by spot modelling. These procedures and
methods may be greatly useful for analysing current TESS and future PLATO data.
