The presence of subparsec binary supermassive black holes (SMBBHs) in the centers of some galaxies is expected, and their mergers are thought to be a key source of nHz gravitational waves. The binary black holes can release electromagnetic radiation in the form of jets, accretion disks, lumps, streams, and circumbinary disks during the inspiral phase, which are affected by numerous hydrodynamic processes like turbulence, shocks, and instabilities. Therefore, the expected oscillation in emission of an SMBBH system caused by binary dynamics is usually hard to detect. Here we present a method based on nonlinear time series analysis designed to detect periodic changes in binary supermassive black hole light curves and illustrate how this can be applied to detect these systems in the universe.