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.

翻译：本文研究分位数向量自回归（QVAR）的估计与模型选择问题。传统分位数回归常产生不理想的交叉分位数曲线，违背了分位数的单调性。为解决该问题，我们提出单纯形分位数向量自回归（SQVAR）框架，将原始QVAR模型的自回归（AR）结构转换为单纯形形式，确保估计的分位数曲线在所有分位数水平上保持单调性。此外，我们在SQVAR模型上施加平滑截断绝对偏差（SCAD）惩罚项以缓解参数空间的爆炸性增长。我们进一步开发了基于贝叶斯信息准则（BIC）的最优惩罚参数选择程序，并提出了用于QVAR模型脉冲响应分析的新框架。最后，我们建立了所提方法的渐近性质，包括估计量的收敛速度与渐近正态性、AR阶数选择的一致性以及基于BIC的惩罚选择的有效性。为说明方法的应用，我们将所提方法应用于美国金融市场数据，突显了SQVAR方法的实用价值。