  We discuss continuous cascade models and their potential for modelling the
energy dissipation in a turbulent flow. Continuous cascade processes, expressed
in terms of stochastic integrals with respect to L\'evy bases, are examples of
ambit processes. These models are known to reproduce experimentally observed
properties of turbulence: The scaling and self-scaling of the correlators of
the energy dissipation and of the moments of the coarse-grained energy
dissipation. We compare three models: a normal model, a normal inverse Gaussian
model and a stable model. We show that the normal inverse Gaussian model is
superior to both, the normal and the stable model, in terms of reproducing the
distribution of the energy dissipation; and that the normal inverse Gaussian
model is superior to the normal model and competitive with the stable model in
terms of reproducing the self-scaling exponents. Furthermore, we show that the
presented analysis is parsimonious in the sense that the self-scaling exponents
are predicted from the one-point distribution of the energy dissipation, and
that the shape of these distributions is independent of the Reynolds number.
