  Superpositions of Ornstein-Uhlenbeck type (supOU) processes provide a rich
class of stationary stochastic processes for which the marginal distribution
and the dependence structure may be modeled independently. We show that they
can also display intermittency, a phenomenon affecting the rate of growth of
moments. To do so, we investigate the limiting behavior of integrated supOU
processes with finite variance. After suitable normalization four different
limiting processes may arise depending on the decay of the correlation function
and on the characteristic triplet of the marginal distribution. To show that
supOU processes may exhibit intermittency, we establish the rate of growth of
moments for each of the four limiting scenarios. The rate change indicates that
there is intermittency, which is expressed here as a change-point in the
asymptotic behavior of the absolute moments.

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