The study of exoplanetary atmospheres epitomises a continuous quest for higher accuracy measurements. Systematic effects and noise associated with both the stellar activity and the instrument can bias the results and thus limit the precision of the analysis. To reach a high photometric and spectroscopic precision, it is therefore essential to correct for these effects. We present here a novel non-parametric approach, named Gaussian Process method for Star Characterization (GPSC), to remove effects of stellar activity and instrumental systematics on planetary signals, with a view to preserve the atmospheric contribution which can be as small as 10$^{-4}$ or even 10$^{-5}$ the flux of the star. We applied our method to data recorded with Kepler, focussing on a sample of lightcurves with different effective temperatures and flux modulations. We found that GPSC can very effectively correct for the short and long term stellar activity and instrumental systematics. Additionally we run the GPSC on both real and simulated transit data, finding transit depths consistent with the original ones. Consequently we considered 10 hours of continuous observations: daily, every other day and weekly, and we used the GPSC to reconstruct the lightcurves. When data are recorded more frequently than once every five days we found that our approach is able to extrapolate the stellar flux at the 10$^{-4}$ level compared to the full stellar flux. These results show a great potential of GPSC to isolate the relevant astrophysical signal and achieve the precision needed for the correction of short and long term stellar activity.
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