  We discuss the effect of the stationarity on the avalanche statistics of
Barkhuasen noise signals. We perform experimental measurements on a
Fe$_{85}$B$_{15}$ amorphous ribbon and compare the avalanche distributions
measured around the coercive field, where the signal is stationary, with those
sampled through the entire hysteresis loop. In the first case, we recover the
scaling exponents commonly observed in other amorphous materials ($\tau=1.3$,
$\alpha=1.5$). while in the second the exponents are significantly larger
($\tau=1.7$, $\alpha=2.2$). We provide a quantitative explanation of the
experimental results through a model for the depinning of a ferromagnetic
domain wall. The present analysis shed light on the unusually high values for
the Barkhausen noise exponents measured by Spasojevic et al. [Phys. Rev. E 54
2531 (1996)].
