论文标题
通过先前的矢量自动加强执行平稳性
Enforcing stationarity through the prior in vector autoregressions
论文作者
论文摘要
平稳性是时间序列分析中非常普遍的假设。且仅当其特征方程的根位于单位圆外时，矢量自回旋过程是静止的，这将自回旋系数矩阵限制为固定区域。但是，固定区域具有高度复杂的几何形状，阻碍了先前分布的规范。在这项工作中，提出了固定矢量自动进程的不受约束的重新聚集化。新参数是部分自相关矩阵，可以解释，并且可以通过简单的奇异值映射到无约束的正方形矩阵的空间。这种转换保留了部分自相关矩阵的各种结构形式，并很容易促进先验的规范。描述了此先验的特性以及一个重要的特殊情况，该案例可与观测矢量中元素的顺序交换。使用Hamiltonian Monte Carlo通过Stan描述和实施后推断和计算。用宏观经济时间序列的应用说明了先前和推论的程序，该程序突出了实施平稳性并鼓励缩小明智的参数结构的好处。本文的补充材料可在“辅助文件”部分中找到。
Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient matrices to lie in the stationary region. However, the stationary region has a highly complex geometry which impedes specification of a prior distribution. In this work, an unconstrained reparameterization of a stationary vector autoregression is presented. The new parameters are partial autocorrelation matrices, which are interpretable, and can be transformed bijectively to the space of unconstrained square matrices through a simple mapping of their singular values. This transformation preserves various structural forms of the partial autocorrelation matrices and readily facilitates specification of a prior. Properties of this prior are described along with an important special case which is exchangeable with respect to the order of the elements in the observation vector. Posterior inference and computation are described and implemented using Hamiltonian Monte Carlo via Stan. The prior and inferential procedures are illustrated with an application to a macroeconomic time series which highlights the benefits of enforcing stationarity and encouraging shrinkage towards a sensible parametric structure. Supplementary materials for this article are available in the ancillary files section.
