Intermittency and infinite variance: the case of integrated supOU processes

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Grahovac, Danijel
Leonenko, Nikolai N.
Taqqu, Murad S.
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Danijel Grahovac, Nikolai N Leonenko, Murad S Taqqu. "Intermittency and infinite variance: the case of integrated supOU processes."
Abstract
SupOU processes are superpositions of Ornstein-Uhlenbeck type processes with a random intensity parameter. They are stationary processes whose marginal distribution and dependence structure can be specified independently. Integrated supOU processes have then stationary increments and satisfy central and non-central limit theorems. Their moments, however, can display an unusual behavior known as ``intermittency''. We show here that intermittency can also appear when the processes have a heavy tailed marginal distribution and, in particular, an infinite variance.
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