Generalized maximum entropy based identification of graphical ARMA models

This paper focuses on the joint estimation of parameters and topologies of multivariate graphical autoregressive moving-average (ARMA) processes. Since the graphical structure of a model can be characterized by the sparsity pattern of its inverse spectral density matrix, a generalized maximum entropy optimization model is derived by imposing a sparse regularization on the inverse spectrum from which the parameters of the AR part and the graph topology can be simultaneously estimated. Then, the whole graphical ARMA model is identified by alternatingly estimating the graphical AR part by solving the regularized maximum entropy problem and the MA part by applying the moment estimation method. The weight to the sparsity regularization term is chosen according to the information theoretic model selection criterion, and simulation examples are provided to illustrate the effectiveness of the proposed identification approach.