Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes
Leonenko, Nikolai N.
Taqqu, Murad S.
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Citation (published version)Danijel Grahovac, Nikolai N Leonenko, Murad S Taqqu. 2019. "Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes." Stochastic Processes and their Applications, Volume 129, Issue 12, pp. 5113-5150. https://doi.org/10.1016/j.spa.2019.01.010
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. In this paper we investigate the limiting behavior of integrated supOU processes with finite variance. We show that after suitable normalization four different limiting processes may arise. The type of limit depends on the decay of the correlation function as well as on the characteristic triplet of the marginal distribution. SupOU processes, moreover, may exhibit intermittency, a phenomenon affecting the rate of growth of moments. We establish this rate for each of the four limiting scenarios. The rate changes at some point indicating that there is a change-point in the asymptotic behavior of absolute moments. For such a behavior to be possible, the moments in the limit theorem do not converge beyond some critical point. We show that this point is related to the dependence stricture of the supOU process.