  Current radial velocity data from specialized instruments contain a large
amount of information that may pass unnoticed if their analysis is not
accurate. The joint use of Bayesian inference tools and frequency analysis has
been shown effective to reveal exoplanets but they have been used less
frequently to investigate stellar activity. We intend to use radial velocity
data of the exoplanet host star GJ 3512 to investigate its magnetic activity.
Our study includes the analysis of the photometric data available. The main
objectives of our work are to constrain the orbital parameters of the
exoplanets in the system, to determine the current level of activity of the
star and to derive an activity cycle length for it. An adaptive importance
sampling method was used to determine the parameters of the exoplanets orbit.
Generalized Lomb-Scargle periodograms were constructed with both radial
velocity curve and photometric data. A careful analysis of the harmonic
frequencies was conducted in each periodogram. Our fit to multiple Keplerian
orbits constrained the orbital parameters of two giant gas planets orbiting the
star GJ 3512. The host star showed an increase of its magnetic activity during
the last observing campaign. The accurate fit of the radial velocity curve data
to the multi-Keplerian orbit permitted to reveal the star rotation in the
residuals of the best fit and estimate an activity cycle length of ~ 14 years.
