  Scaling properties of time series are usually studied in terms of the scaling
laws of empirical moments, which are the time average estimates of moments of
the dynamic variable. Nonlinearities in the scaling function of empirical
moments are generally regarded as a sign of multifractality in the data. We
show that, except for the Brownian motion, this method fails to disclose the
correct monofractal nature of self-similar L\'evy processes. We prove that for
this class of processes it produces apparent multifractality characterised by a
piecewise-linear scaling function with two different regimes, which match at
the stability index of the considered process. This result is motivated by
previous numerical evidence. It is obtained by introducing an appropriate
stochastic normalisation which is able to cure empirical moments, without
hiding their dependence on time, when moments they aim at estimating do not
exist.
