Quantile regression continues to increase in usage, providing a useful alternative to customary mean regression. Primary implementation takes the form of so-called multiple quantile regression, creating a separate regression for each quantile of interest. However, recently, advances have been made in joint quantile regression, supplying a quantile function which avoids crossing of the regression across quantiles. Here, we turn to quantile autoregression (QAR), offering a fully Bayesian version. We extend the initial quantile regression work of Koenker and Xiao (2006) in the spirit of Tokdar and Kadane (2012). We offer a directly interpretable parametric model specification for QAR. Further, we offer a p-th order QAR(p) version, a multivariate QAR(1) version, and a spatial QAR(1) version. We illustrate with simulation as well as a temperature dataset collected in Arag\'on, Spain.

翻译：摘要：分位数回归的应用日益广泛，为传统均值回归提供了有价值的替代方案。其主要实现形式为所谓的多分位数回归，即对每个感兴趣的分位数分别建立回归模型。然而，近期联合分位数回归取得了进展，该技术能提供一种避免分位数间回归曲线交叉的分位数函数。本文研究分位数自回归（QAR），并提出了一个全贝叶斯框架。我们借鉴Tokdar与Kadane（2012）的思路，对Koenker与Xiao（2006）的初始分位数回归工作进行了拓展。我们为QAR提供了一个可直接解释的参数模型规范，并进一步提出了p阶QAR(p)模型、多元QAR(1)模型以及空间QAR(1)模型。通过模拟实验以及来自西班牙阿拉贡地区的气温数据集，我们对这些模型进行了验证。