Vector autoregressions (VARs) are popular in analyzing 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 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. In the application of the US macroeconomic data, our models outperform standard VARs in point and density forecasting and yield a summary of the US economic dynamic.

翻译：向量自回归（VAR）在分析经济时间序列中应用广泛。然而，当变量数量和滞后阶数适中偏大时，VAR可能出现过度参数化问题。张量VAR作为近期提出的应对过度参数化的方案，将系数矩阵视为三阶张量，并通过估计相应的张量分解来实现模型简约性。本文采用基于CANDECOMP/PARAFAC（CP）分解的张量VAR结构，并运用贝叶斯推断进行参数估计。首先，我们通过向边际分量（即分解中的元素）施加乘法伽马先验来确定秩，并采用自适应推断方案加速计算。其次，为获得可解释的边际分量，我们提出一种交织算法以改善边际分量的混合效果。在美国宏观经济数据的应用中，我们的模型在点预测和密度预测方面均优于标准VAR，并有效总结了美国经济动态特征。