Fixed-smoothing Uniform Inference for Quantile Regression
Abstract
This paper develops fixed-smoothing (fixed-b, fixed-K) inference methods for time-series quantile regression that are robust to heteroskedasticity and autocorrelation. Our approach is uniformly valid over quantile levels and accounts for dependence both over time and across quantiles. It enables the construction of uniform confidence bands, Wald, and Sup-t tests for joint hypotheses, and tests of shape restrictions, providing a unified framework for assessing heterogeneity in quantile effects. A key challenge is that, under weak dependence, uniform inference for quantile regression processes is generally non-pivotal because the limiting distributions depend on the long-run covariance structure across quantiles. To address this issue, we develop two complementary approaches. The uniform-in-τ method estimates the covariance structure and simulates the non-pivotal limiting distribution. For certain tests involving a finite collection of quantile levels, the stack-Wald method delivers pivotal fixed-smoothing inference. We establish the asymptotic validity of both approaches. Simulation results show that the proposed methods substantially improve size control relative to existing HAC-based procedures while maintaining good power. An application to predictive quantile regressions for stock returns reveals substantial heterogeneity in predictive effects across both quantiles and forecast horizons.
Related
- Conformalized Quantile Regression and Minimax Limits of Fixed-Score Calibration under Known Covariate Shift
- Quantile-Only Regression: Inference and Partial Identification under Quantile Disclosure
- Distributed Selective Inference for Quantile Regression
- Bias Correction and Inference for Panel Quantile Regression
- Statistical inference for quantile correlation regression with bivariate outcomes
BibTeX
@misc{chen2026fixedsmoothing,
title = {{Fixed-smoothing Uniform Inference for Quantile Regression}},
author = {Kaicheng Chen and Antonio F. Galvao and Seunghwa Rho and Timothy J. Vogelsang and Jungmo Yoon},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05883},
eprint = {2609.05883},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05883},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fixed-smoothing Uniform Inference for Quantile Regression
AU - Kaicheng Chen
AU - Antonio F. Galvao
AU - Seunghwa Rho
AU - Timothy J. Vogelsang
AU - Jungmo Yoon
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05883
UR - https://arxiv.org/abs/2609.05883
AB - This paper develops fixed-smoothing (fixed-b, fixed-K) inference methods for time-series quantile regression that are robust to heteroskedasticity and autocorrelation. Our approach is uniformly valid over quantile levels and accounts for dependence both over time and across quantiles. It enables the construction of uniform confidence bands, Wald, and Sup-t tests for joint hypotheses, and tests of shape restrictions, providing a unified framework for assessing heterogeneity in quantile effects. A key challenge is that, under weak dependence, uniform inference for quantile regression processes is generally non-pivotal because the limiting distributions depend on the long-run covariance structure across quantiles. To address this issue, we develop two complementary approaches. The uniform-in-τ method estimates the covariance structure and simulates the non-pivotal limiting distribution. For certain tests involving a finite collection of quantile levels, the stack-Wald method delivers pivotal fixed-smoothing inference. We establish the asymptotic validity of both approaches. Simulation results show that the proposed methods substantially improve size control relative to existing HAC-based procedures while maintaining good power. An application to predictive quantile regressions for stock returns reveals substantial heterogeneity in predictive effects across both quantiles and forecast horizons.
ER -