Identification of multivariate AR-models by threshold accepting

In econometric modelling the choice of relevant variables is of crucial importance for the Interpretation of the results. In many cases it is based on some a priori knowledge from economic theory and a rather heuristic procedure for determining other influential variables sometimes based on an Information criterion. This paper deals with an automatic method for the identification of relevant variables based solely on an Information criterion. As an example, the identification of multivariate lag structures in AR-models is studied. This issue arises e.g. for large-scale econometric models, for Granger causality tests or the application of Johansen's test for cointegration. The procedure suggested in this paper allows the optimization of the lag structure over the whole set of possible multivariate lag structures with regard to a given information criterion, e.g. the Hannan-Quinn estimator or Akaike's final prediction error criterion. The optimization is performed by the heuristic multiple purpose optimization algorithm Threshold Accepting which proved to be very successful for discrete optimization problems in economics and econometrics. The implementation of Threshold Accepting for subset identification in multivariate AR-models and some Simulation results for a bivariate model are presented.