Invertibility of infinitely divisible continuous-time moving average processes

TL;DR

This paper investigates the conditions under which continuous-time moving average processes driven by Lévy processes can be inverted to recover the original noise, based on kernel properties and Lévy triplet characteristics.

Contribution

It provides new sufficient conditions for invertibility of such processes, linking kernel and Lévy process parameters to noise recoverability.

Findings

Sufficient conditions for invertibility are established.

Invertibility depends on kernel and Lévy triplet properties.

Results enable noise recovery in continuous-time models.

Abstract

This paper studies the invertibility property of continuous time moving average processes driven by a L\'evy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel involved and the characteristic triplet of the background driving L\'evy process.