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The Local Projection Residual Bootstrap for AR(1) Models

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  • Amilcar Velez

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. 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.

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  • Amilcar Velez, 2023. "The Local Projection Residual Bootstrap for AR(1) Models," Papers 2309.01889, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2309.01889
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