The unusual properties of aggregated superpositions of Ornstein-Uhlenbeck type processes

TL;DR

This paper investigates the unusual asymptotic properties of aggregated supOU processes, revealing unexpected growth rates in moments and cumulants, and introduces the concept of intermittency in these processes.

Contribution

It characterizes the asymptotic behavior of integrated and partial sum supOU processes and identifies intermittency as a key property.

Findings

SupOU processes exhibit fast growth of moments and cumulants.

The asymptotic behavior of supOU processes is more complex than classical models.

Intermittency is identified as a fundamental property of aggregated supOU processes.

Abstract

Superpositions of Ornstein-Uhlenbeck type (supOU) processes form a rich class of stationary processes with a flexible dependence structure. The asymptotic behavior of the integrated and partial sum supOU processes can be, however, unusual. Their cumulants and moments turn out to have an unexpected rate of growth. We identify the property of fast growth of moments or cumulants as intermittency.