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

TL;DR

This paper analyzes the clustering behavior of large deviation events in infinite moving average processes with finite exponential moments, focusing on the short memory regime.

Contribution

It provides a detailed description of the clustering of large deviations in moving average processes within the short memory regime, a novel analysis in this context.

Findings

Characterization of large deviation clusters in short memory processes

Conditions under which large deviations tend to cluster

Insights into the probabilistic structure of deviations in moving averages

Abstract

We describe the cluster of large deviations events that arise when one such large deviations event occurs. We work in the framework of an infinite moving average process with a noise that has finite exponential moments.