  We study the average shape of a fluctuation of a time series x(t), that is
the average value <x(t)-x(0)>_T before x(t) first returns, at time T, to its
initial value x(0). For large classes of stochastic processes we find that a
scaling law of the form <x(t) - x(0)>_T = T^\alpha f(t/T) is obeyed. The
scaling function f(s) is to a large extent independent of the details of the
single increment distribution, while it encodes relevant statistical
information on the presence and nature of temporal correlations in the process.
We discuss the relevance of these results for Barkhausen noise in magnetic
systems.
