  Different methods are used to determine the scaling exponents associated with
a time series describing a complex dynamical process, such as those observed in
geophysical systems. Many of these methods are based on the numerical
evaluation of the variance of a diffusion process whose step increments are
generated by the data. An alternative method focuses on the direct evaluation
of the scaling coefficient of the Shannon entropy of the same diffusion
distribution. The combined use of these methods can efficiently distinguish
between fractal Gaussian and L\'{e}vy-walk time series and help to discern
between alternative underling complex dynamics.
