This paper extends the horseshoe prior of Carvalho et al. (2010) to Bayesian quantile regression (HS-BQR) and provides a fast sampling algorithm for computation in high dimensions. The performance of the proposed HS-BQR is evaluated on Monte Carlo simulations and a high dimensional Growth-at-Risk (GaR) forecasting application for the U.S. The Monte Carlo design considers several sparsity and error structures. Compared to alternative shrinkage priors, the proposed HS-BQR yields better (or at worst similar) performance in coefficient bias and forecast error. The HS-BQR is particularly potent in sparse designs and in estimating extreme quantiles. As expected, the simulations also highlight that identifying quantile specific location and scale effects for individual regressors in dense DGPs requires substantial data. In the GaR application, we forecast tail risks as well as complete forecast densities using the McCracken and Ng (2020) database. Quantile specific and density calibration score functions show that the HS-BQR provides the best performance, especially at short and medium run horizons. The ability to produce well calibrated density forecasts and accurate downside risk measures in large data contexts makes the HS-BQR a promising tool for nowcasting applications and recession modelling.

翻译：本文扩展了Carvalho等人(2010年)之前的马蹄铁,将卡瓦尔霍等人(2010年)延伸到巴耶斯四分位回归(HS-BQR),并为高度计算提供了快速抽样算法。拟议HS-BQR的性能在蒙特卡洛模拟和高维度增长-风险(GaR)美国预测应用程序上进行了评估。蒙特卡洛设计考虑了几个宽度和误差结构。与替代缩缩微前科相比,拟议的HS-BQR在系数偏差和预测错误方面产生更好的(或最相似的)性能。HS-BQR在稀疏设计和估计极端四分位方面特别强。正如所预期的那样,模拟还突出表明,确定密度高度DGP中个人递增者的具体位置和规模影响需要大量数据。在加热点应用中,我们利用麦克拉肯和恩(202020年)数据库预测尾部风险以及完整的预测密度密度。具体和密度校准分数函数显示,HS-B公司现在提供了最佳的性设计和中度模型定位模型环境中高度预测。