The effect of memory on functional large deviations of infinite moving average processes

TL;DR

This paper investigates how the decay rate of coefficients in infinite moving average processes influences their large deviation behaviors across functional, moderate, and huge deviation regimes.

Contribution

It provides a detailed analysis of the impact of coefficient decay rates on the large deviation principles of infinite moving average processes.

Findings

Large deviations resemble i.i.d. sequences when coefficients decay rapidly.

Slow decay of coefficients leads to significant changes in large deviation behavior.

The study covers functional, moderate, and huge deviation principles.

Abstract

The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change dramatically. We study this phenomenon in the context of functional large, moderate and huge deviation principles.