  We address the generic problem of extracting the scaling exponents of a
stationary, self-affine process realised by a timeseries of finite length,
where information about the process is not known a priori. Estimating the
scaling exponents relies upon estimating the moments, or more typically
structure functions, of the probability density of the differenced timeseries.
If the probability density is heavy tailed, outliers strongly influence the
scaling behaviour of the moments. From an operational point of view, we wish to
recover the scaling exponents of the underlying process by excluding a minimal
population of these outliers. We test these ideas on a synthetically generated
symmetric alpha-stable Levy process and show that the Levy exponent is
recovered in up to the 6th order moment after only ~0.1-0.5% of the data are
excluded. The scaling properties of the excluded outliers can then be tested to
provide additional information about the system.
