Abstract

Matrix-variate time series are now common in economic, medical, environmental, and atmospheric sciences, typically associated with large matrix dimensions. We introduce a structured autoregressive (AR) model to characterize temporal dynamics in a matrix-variate time series by formulating the AR matrices in a bilinear form. This bilinear parameter structure reduces the model dimension and highlights dynamic interaction among columns and rows in the AR matrices, making the model highly explainable. We further incorporate spatial information and explore sparsity in the AR coefficients by introducing spatial neighborhoods. In addition, we consider a nonstationary multi-resolution spatial covariance model for innovation errors. The resulting spatio-temporal AR model is flexible in capturing heterogeneous spatial and temporal features while maintaining a parsimonious parameterization. The model parameters are estimated by maximum likelihood (ML) with a fast algorithm developed for computation. We conduct a simulation study and present an application to a wind-speed dataset to demonstrate the merits of our methodology. Supplementary files for this article are available online.

摘要

矩阵变量时间序列现在在经济、医学、环境和大气科学中很常见，通常与大矩阵维度相关联。我们引入了结构化自回归 (AR) 模型，通过以双线性形式制定 AR 矩阵来表征矩阵变量时间序列中的时间动态。这种双线性参数结构降低了模型维度，突出了 AR 矩阵中列和行之间的动态交互，使模型具有高度可解释性。我们通过引入空间邻域进一步结合空间信息并探索 AR 系数中的稀疏性。此外，我们考虑了用于创新误差的非平稳多分辨率空间协方差模型。由此产生的时空 AR 模型可以灵活地捕捉异构空间和时间特征，同时保持简约的参数化。模型参数通过最大似然 (ML) 和为计算开发的快速算法进行估计。我们进行了一项模拟研究，并提出了一个风速数据集的应用程序，以证明我们方法的优点。本文的补充文件可在线获取。