Quantile Vector Autoregression without Crossing

TL;DR

This paper introduces a novel SQVAR framework that ensures monotonic quantile curves in vector autoregression models, addressing crossing issues and enhancing model stability with theoretical guarantees and practical applications.

Contribution

We propose the simplex quantile vector autoregression (SQVAR) framework with SCAD penalty and BIC-based model selection, ensuring monotonicity and stability in QVAR estimation.

Findings

SQVAR effectively prevents crossing quantile curves.

The method demonstrates strong asymptotic properties.

Application to U.S. financial data shows practical usefulness.

Abstract

This paper considers estimation and model selection of quantile vector autoregression (QVAR). Conventional quantile regression often yields undesirable crossing quantile curves, violating the monotonicity of quantiles. To address this issue, we propose a simplex quantile vector autoregression (SQVAR) framework, which transforms the autoregressive (AR) structure of the original QVAR model into a simplex, ensuring that the estimated quantile curves remain monotonic across all quantile levels. In addition, we impose the smoothly clipped absolute deviation (SCAD) penalty on the SQVAR model to mitigate the explosive nature of the parameter space. We further develop a Bayesian information criterion (BIC)-based procedure for selecting the optimal penalty parameter and introduce new frameworks for impulse response analysis of QVAR models. Finally, we establish asymptotic properties of the proposed method, including the convergence rate and asymptotic normality of the estimator, the consistency of AR order selection, and the validity of the BIC-based penalty selection. For illustration, we apply the proposed method to U.S. financial market data, highlighting the usefulness of our SQVAR method.