Estimation of VAR Models: Computational Aspects

The Vector Autoregressive (VAR) model with zero coefficient restrictions can be formulated as a Seemingly Unrelated Regression Equation (SURE) model. Both the response vectors and the coefficient matrix of the regression equations comprise columns from a Toeplitz matrix. Efficient numerical and computational methods which exploit the Toeplitz and Kronecker product structure of the matrices are proposed. The methods are also adapted to provide numerically stable algorithms for the estimation of VAR(p) models with Granger-caused variables.