# Intermittency and infinite variance: the case of integrated supOU processes

## TL;DR

This paper investigates integrated supOU processes, revealing that they can exhibit intermittency even with heavy-tailed, infinite variance distributions, expanding understanding of their complex statistical behaviors.

## Contribution

It demonstrates that intermittency occurs in integrated supOU processes with heavy-tailed, infinite variance marginals, a novel insight into their stochastic properties.

## Key findings

- Intermittency can occur with heavy-tailed, infinite variance distributions.
- Integrated supOU processes satisfy limit theorems with complex behaviors.
- Heavy tails influence the moments and dependence structure.

## 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.