Inference in Predictive Quantile Regressions

TL;DR

This paper develops new inference methods for predictive quantile regressions with near-unit root regressors, introducing a switching-FM test that adapts to the predictor's persistence level, and demonstrates its effectiveness through simulations and stock return data.

Contribution

It derives asymptotic distributions for quantile regression estimators with near-unit root predictors and proposes a novel switching-FM predictive test for quantile predictability.

Findings

The switching-FM test maintains reliable size and good power in small samples.

The methodology effectively predicts stock return distribution quantiles using persistent regressors.

Simulations confirm the test's robustness across different persistence levels.

Abstract

This paper studies inference in predictive quantile regressions when the predictive regressor has a near-unit root. We derive asymptotic distributions for the quantile regression estimator and its heteroskedasticity and autocorrelation consistent (HAC) t-statistic in terms of functionals of Ornstein-Uhlenbeck processes. We then propose a switching-fully modified (FM) predictive test for quantile predictability. The proposed test employs an FM style correction with a Bonferroni bound for the local-to-unity parameter when the predictor has a near unit root. It switches to a standard predictive quantile regression test with a slightly conservative critical value when the largest root of the predictor lies in the stationary range. Simulations indicate that the test has a reliable size in small samples and good power. We employ this new methodology to test the ability of three commonly employed, highly persistent and endogenous lagged valuation regressors - the dividend price ratio, earnings price ratio, and book-to-market ratio - to predict the median, shoulders, and tails of the stock return distribution.