Spectral bootstrap confidence bands for L\'evy-driven moving average processes

TL;DR

This paper develops spectral bootstrap methods to construct confidence bands for the Le9vy density of a driving process in high-frequency observed Le9vy-driven moving average models, ensuring asymptotic validity.

Contribution

It introduces a new spectral estimator and bootstrap procedures for Le9vy density inference, with theoretical guarantees for their asymptotic correctness.

Findings

Bootstrap confidence bands are asymptotically valid.

Proposed methods perform well on high-frequency data.

Confidence bands are constructed away from the origin.

Abstract

In this paper we study the problem of constructing bootstrap confidence intervals for the L\'evy density of the driving L\'evy process based on high-frequency observations of a L\'evy-driven moving average processes. Using a spectral estimator of the L\'evy density, we propose a novel implementations of multiplier and empirical bootstraps to construct confidence bands on a compact set away from the origin. We also provide conditions under which the confidence bands are asymptotically valid.