Asymptotic Theory for Unit Root Moderate Deviations in Quantile Autoregressions and Predictive Regressions

TL;DR

This paper develops the asymptotic theory for quantile autoregressions with parameters near the unit boundary, including near-stationary and near-explosive cases, and provides finite-sample performance insights through simulations.

Contribution

It extends existing asymptotic frameworks to quantile autoregressions with parameters close to the unit boundary, incorporating quantile-dependent parameters and deriving new limiting distributions.

Findings

Serial correlation coefficient converges to a ratio of two independent variables

Monte Carlo simulations demonstrate finite-sample estimation performance

Bahadur-type representation derived for quantile model parameters

Abstract

We establish the asymptotic theory in quantile autoregression when the model parameter is specified with respect to moderate deviations from the unit boundary of the form (1 + c / k) with a convergence sequence that diverges at a rate slower than the sample size n. Then, extending the framework proposed by Phillips and Magdalinos (2007), we consider the limit theory for the near-stationary and the near-explosive cases when the model is estimated with a conditional quantile specification function and model parameters are quantile-dependent. Additionally, a Bahadur-type representation and limiting distributions based on the M-estimators of the model parameters are derived. Specifically, we show that the serial correlation coefficient converges in distribution to a ratio of two independent random variables. Monte Carlo simulations illustrate the finite-sample performance of the estimation procedure under investigation.