  We study the limiting behavior of continuous time trawl processes which are
defined using an infinitely divisible random measure of a time dependent set.
In this way one is able to define separately the marginal distribution and the
dependence structure. One can have long-range dependence or short-range
dependence by choosing the time set accordingly. We introduce the scaling
function of the integrated process and show that its behavior displays
intermittency, a phenomenon associated with an unusual behavior of moments.
