Estimating all possible SUR models with permuted exogenous data matrices derived from a VAR process

The Vector Autoregressive (VAR) process with zero coefficient constraints can be formulated as a Seemingly Unrelated Regressions (SUR) model. Within the context of subset VAR model selection a computationally efficient strategy to generate and estimate all G! SUR models when permuting the exogenous data matrices is proposed, where G is the number of the regression equations. The combinatorial algorithm is based on orthogonal transformations, exploits the particular structure of the modified models and avoids the estimation of these models afresh by utilizing previous computation. Theoretical measurements of complexity are derived to prove the efficiency of the proposed algorithm.