Periodic behaviour of reputation time series is investigated by Fourier series approximations. Harmonics of increasing frequency are successively added to an initial base harmonic until a stop criterion is triggered. The stop condition is determined by formulating a novel ‘sufficient convergence’ criterion based on an error bound when approximating discrete data by a Fourier aeries. The results show that 70% of a sample of 130 reputation time series exhibited periodic effects with a period between 30 and 80 days, with mean 45 days and standard deviation 55 days. 3.8% were deemed to have no periodic effect. Loess validation produced similar figures. The implication is that reputational events are active for approximately one to three months.