Autoregressive Identification of Kronecker Graphical Models

We address the problem to estimate a Kronecker graphical model corresponding to an autoregressive Gaussian stochastic process. The latter is completely described by the power spectral density function whose inverse has support which admits a sparse Kronecker product decomposition. We propose a Bayesian approach to estimate such a model. We test the effectiveness of the proposed method by some numerical experiments. We also apply the procedure to urban pollution monitoring data.