Optimized Multivariate Lag Structure Selection

Model selection - choosing the relevant variables and structures - is a central task in econometrics. Given a limited number of observations, estimation and inference depend on this choice. A frequently treated model-selection problem arises in multivariate autoregressive models, where the problem reduces to the choice of a dynamic structure. In most applications this choice is based either on some ad hoc procedure or on a search within a very small subset of all possible models. In this paper the selection is performed using an explicit optimization approach for a given information criterion. Since complete enumeration of all possible lag structures is infeasible even for moderate dimensions, the global optimization heuristic of threshold accepting is implemented. A simulation study compares this approach with the standard `take all up to the kth lagʹ approach. It is found that, if the lag structure of the true model is sparse, the threshold accepting optimization approach gives far better approximations.