The aim of my research is to shed light on the physical processes taking place in the surroundings of black holes and neutron stars, the most extreme objects known in the Universe. When matter falls on these collapsed stars, the conversion of gravitational potential into electromagnetic radiation (also known as "accretion") always leads to turbulent motion. This turbulence produces strong stochastic variability in the emitted radiation, which encodes critical properties about the physical conditions and dynamical processes shaping these extreme environments. By using advanced time series analysis techniques, we can extract key insights into the structure of matter in strong gravitational fields and the mechanisms driving these extreme phenomena.