  We present an $i$-band photometric study of over 800 young stellar objects in
the OB association Cep OB3b, which samples timescales from 1 minute to ten
years. Using structure functions we show that on all timescales ($\tau$) 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
($\tau^{0.8}$) in variability from timescales of a few minutes to ten years.
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
timescale corresponding to the rotational period of the star, with little
additional variability beyond that timescale. However, about a third of the
Class IIs show lower overall variability, but their variability is still
increasing at 10 years. 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-timescale 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
datasets (the "fast structure function"), based on fast Fourier transforms.
