Estimating seemingly unrelated regression models with vector autoregressive disturbances

The numerical solution of seemingly unrelated regression (SUR) models with vector autoregressive disturbances is considered. Initially, an orthogonal transformation is applied to reduce the model to one with smaller dimensions. The transformed model is expressed as a reduced-size SUR model with stochastic constraints. The generalized QR decomposition is used as the main computational tool to solve this model. An iterative estimation algorithm is proposed when the variance-covariance matrix of the disturbances and the matrix of autoregressive coefficients are unknown. Strategies to compute the orthogonal factorizations of the non-dense-structured matrices which arise in the estimation procedure are presented. Experimental results demonstrate the computational efficiency of the proposed algorithm