Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes

TL;DR

This paper studies integrated supOU processes, revealing their potential for intermittency through different limiting behaviors of moments, depending on correlation decay and distribution characteristics.

Contribution

It introduces a comprehensive analysis of the limiting behavior of integrated supOU processes, highlighting their capacity for intermittency and moment growth rate changes.

Findings

Four different limiting processes identified based on correlation decay and distribution.

Intermittency demonstrated through change-points in the asymptotic behavior of moments.

Rate of growth of moments varies, indicating complex dependence structures.

Abstract

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.