We compare quasar selection techniques based on their optical variability using data from the Catalina Real-time Transient Survey (CRTS). We introduce a new technique based on Slepian wavelet variance (SWV) that shows comparable or better performance to structure functions and damped random walk models but with fewer assumptions. Combining these methods with WISE mid-IR colors produces a highly efficient quasar selection technique which we have validated spectroscopically. The SWV technique also identifies characteristic timescales in a time series and we find a characteristic rest frame timescale of ~54 days, confirmed in the light curves of ~18000 quasars from CRTS, SDSS and MACHO data, and anticorrelated with absolute magnitude. This indicates a transition between a damped random walk and $P(f) propto f^{-1⁄3}$ behaviours and is the first strong indication that a damped random walk model may be too simplistic to describe optical quasar variability.