Optimized Multivariate Lag Structure Selection

Abstract

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 treatedmodel-selection problem arises in multivariate autoregressive models, wherethe problem reduces to the choice of a dynamic structure. In most applicationsthis choice is based either on some ad hoc procedure or on a search within avery small subset of all possible models. In this paper the selection isperformed using an explicit optimization approach for a given informationcriterion. Since complete enumeration of all possible lag structures isinfeasible even for moderate dimensions, the global optimization heuristic ofthreshold accepting is implemented. A simulation study compares this approachwith the standard `take all up to the kth lag' approach. It is foundthat, if the lag structure of the true model is sparse, the thresholdaccepting optimization approach gives far better approximations.