Prediction intervals for quantile autoregression

TL;DR

This paper develops new methods for constructing prediction intervals in autoregressive models using quantile techniques and bootstrap schemes, improving coverage and efficiency.

Contribution

It introduces novel quantile-based prediction interval methods for both classical and modern autoregressive models, validated by theory and simulations.

Findings

Improved coverage properties over existing methods

Enhanced computational efficiency

Effective application to economic data

Abstract

This paper introduces new methods for constructing prediction intervals using quantile-based techniques. The procedures are developed for both classical (homoscedastic) autoregressive models and modern quantile autoregressive models. They combine quantile estimation with multiplier bootstrap schemes to approximate the sampling variability of coefficient estimates, together with bootstrap replications of future observations. We consider both percentile-based and predictive-root-based constructions. Theoretical results establish the validity and pertinence of the proposed methods. Simulation experiments evaluate their finite-sample performance and show that the proposed methods yield improved coverage properties and computational efficiency relative to existing approaches in the literature. The empirical usefulness of the methods is illustrated through applications to U.S. unemployment rate data and retail gasoline prices.