论文标题
通过张量分解的矢量自动测得的贝叶斯推断
Bayesian inference of vector autoregressions with tensor decompositions
论文作者
论文摘要
向量自动加工（VAR）是分析多元经济时间序列的流行模型。但是，如果变量和滞后的数量适中大，则可以过度参数化。 Tensor VAR是最近用于过度参数化的解决方案，将系数矩阵视为三阶张量，并估计相应的张量分解以实现parsimony。在本文中，我们采用张量var结构进行candecomp/parafac（CP）分解，并进行贝叶斯推断以估计参数。首先，我们通过在张量边缘（即分解中的元素）之前施加乘法伽玛来确定等级，并使用适应性推论方案加速计算。其次，为了获得可解释的边缘，我们提出了一种交织算法，以改善边缘的混合，并使用后处理程序确定边缘。在美国宏观经济数据的应用中，我们的模型在点和密度预测上都优于标准VAR，并得出了美国经济动态的摘要。
Vector autoregressions (VARs) are popular model for analyzing multivariate economic time series. However, VARs can be over-parameterized if the numbers of variables and lags are moderately large. Tensor VAR, a recent solution to over-parameterization, treats the coefficient matrix as a third-order tensor and estimates the corresponding tensor decomposition to achieve parsimony. In this paper, we employ the Tensor VAR structure with a CANDECOMP/PARAFAC (CP) decomposition and conduct Bayesian inference to estimate parameters. Firstly, we determine the rank by imposing the Multiplicative Gamma Prior to the tensor margins, i.e. elements in the decomposition, and accelerate the computation with an adaptive inferential scheme. Secondly, to obtain interpretable margins, we propose an interweaving algorithm to improve the mixing of margins and identify the margins using a post-processing procedure. In an application to the US macroeconomic data, our models outperform standard VARs in point and density forecasting and yield a summary of the dynamic of the US economy.
