The Local Projection Residual Bootstrap for AR(1) Models

TL;DR

This paper introduces a novel local projection residual bootstrap method for AR(1) models, enabling more accurate confidence intervals for impulse response coefficients, especially under complex conditions like unit roots and heteroskedasticity.

Contribution

It develops a new bootstrap approach based on local projections for AR(1) models, with theoretical guarantees and improved confidence interval accuracy.

Findings

Proves uniform consistency of the bootstrap over a broad class of AR(1) models.

Establishes the asymptotic validity of the confidence intervals.

Demonstrates asymptotic refinements for certain AR(1) models.

Abstract

This paper proposes a local projection residual bootstrap method to construct confidence intervals for impulse response coefficients of AR(1) models. Our bootstrap method is based on the local projection (LP) approach and involves a residual bootstrap procedure applied to AR(1) models. We present theoretical results for our bootstrap method and proposed confidence intervals. First, we prove the uniform consistency of the LP-residual bootstrap over a large class of AR(1) models that allow for a unit root, conditional heteroskedasticity of unknown form, and martingale difference shocks. Then, we prove the asymptotic validity of our confidence intervals over the same class of AR(1) models. Finally, we show that the LP-residual bootstrap provides asymptotic refinements for confidence intervals on a restricted class of AR(1) models relative to those required for the uniform consistency of our bootstrap.