ABSTRACT We present an i-band photometric study of over 800 young stellar objects in the OB association Cep OB3b, which samples time-scales from one minute to 10 yr. Using structure functions we show that on all time-scales (τ) there is a monotonic decrease in variability from Class I to Class II through the transition disc (TD) systems to Class III, i.e. the more evolved systems are less variable. The Class Is show an approximately power-law increase (τ0.8) in variability from time-scales of a few minutes to 10 yr. The Class II, TDs, and Class III systems show a qualitatively different behaviour with most showing a power-law increase in variability up to a time-scale corresponding to the rotational period of the star, with little additional variability beyond that time-scale. However, about a third of the Class IIs shows lower overall variability, but their variability is still increasing at 10 yr. This behaviour can be explained if all Class IIs have two primary components to their variability. The first is an underlying roughly power-law variability spectrum, which evidence from the infrared suggests is driven by accretion rate changes. The second component is approximately sinusoidal and results from the rotation of the star. We suggest that the systems with dominant longer time-scale variability have a smaller rotational modulation either because they are seen at low inclinations or have more complex magnetic field geometries. We derive a new way of calculating structure functions for large simulated data sets (the ‘fast structure function’), based on fast Fourier transforms.