  We consider a parametrised perturbation of a $\mathscr C^r$ diffeomorphism on
a closed smooth Riemannian manifold with $r\geq 1$, modeled by nonautonomous
dynamical systems. A point without time averages for a (nonautonomous)
dynamical system is said to have historic behaviour. It is known that for any
$\mathscr C^r$ diffeomorphism, the observability of historic behaviour, in the
sense of the existence of a positive Lebesgue measure set consisting of points
with historic behaviour, disappears under absolutely continuous, independent
and identically distributed (i.i.d.) noise. On contrast, we show that the
observability of historic behaviour can appear by a non-i.i.d. noise: we
consider a contraction mapping for which the set of points with historic
behaviour is of zero Lebesgue measure and provide an absolutely continuous,
non-i.i.d. noise under which the set of points with historic behaviour is of
positive Lebesgue measure.
