Intermittency of trawl processes

TL;DR

This paper investigates the limiting behavior of continuous time trawl processes, highlighting how their moments exhibit intermittency due to the dependence structure and the scaling function of the integrated process.

Contribution

It introduces the concept of intermittency in trawl processes and analyzes how the scaling function reveals unusual moment behavior based on dependence structure.

Findings

Demonstrates the presence of intermittency in trawl processes

Shows how dependence structure affects the scaling behavior

Provides a framework for analyzing moments of integrated processes

Abstract

We study the limiting behavior of continuous time trawl processes which are defined using an infinitely divisible random measure of a time dependent set. In this way one is able to define separately the marginal distribution and the dependence structure. One can have long-range dependence or short-range dependence by choosing the time set accordingly. We introduce the scaling function of the integrated process and show that its behavior displays intermittency, a phenomenon associated with an unusual behavior of moments.