On Constrained Estimation of Graphical Time Series Models

Graphical time series models encode the conditional independence among the variables of a multivariate time series. An iterative method is proposed to estimate a graphical time series model based on a sparse vector autoregressive process. The method estimates both the autoregressive coefficients and the inverse of noise covariance matrix under sparsity constraints on both the coefficients and the inverse covariance matrix. This iterative method estimates a sparse vector autoregressive model by considering maximum likelihood estimation with the sparsity constraints as a biconcave problem, where the optimization problem becomes concave when either the autoregressive coefficients or the inverse noise covariance matrix is fixed. The method also imposes fewer restrictions in the estimation comparing to the use of a structural vector autoregressive model to study the dynamic interdependencies between time series variables.