Clustering of large deviations in moving average processes: the long memory regime

TL;DR

This paper studies how rare large deviations cluster in long-memory moving average processes, revealing that cluster sizes are governed by the hitting times of a shifted fractional Brownian motion with drift.

Contribution

It introduces a novel analysis of large deviation clustering in long-memory processes using fractional Brownian motion models.

Findings

Cluster sizes increase with long memory effects

Asymptotic cluster behavior is described by hitting times of fractional Brownian motion

Long memory significantly influences the structure of large deviations

Abstract

We investigate how large deviations events cluster in the framework of an infinite moving average process with light-tailed noise and long memory. The long memory makes clusters larger, and the asymptotic behaviour of the size of the cluster turns out to be described by the first hitting time of a randomly shifted fractional Brownian motion with drift.