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This study examines high-dimensional time series data presented in matrix format. We address two primary challenges inherent in high-dimensional data analysis: reducing dimensionality and identifying active structures within matrix autoregressive (MAR) models. Moving beyond traditional variable-level analysis, we incorporate prior knowledge by considering both the individual variables and the group structures of the coefficient matrices. To achieve this, we introduce efficient Bayesian structure selection approaches. Under the assumption of sparsity, we adopt a spike-and-slab prior—constructed as a mixture of a point mass at zero and a normal distribution—and incorporate a latent indicator variable to represent the structural status within the MAR framework. Furthermore, we develop an efficient Gibbs sampling algorithm that uses the median probability criterion to identify active structures for Bayesian inference. We also establish the theoretical consistency of our selection approach. Simulation studies demonstrate the computational efficiency and selection performance of the proposed methods, and real-world data analysis confirms their practical effectiveness for concurrent variable and group selection. Finally, based on the maximum a posteriori principle, we also propose an Expectation-Maximization (EM)-type structure selection method.

More information: https://sites.google.com/view/ray-bingchenswebsite/