Subset selection for vector autoregressive processes via adaptive Lasso

Subset selection is a critical component of vector autoregressive (VAR) modeling. This paper proposes simple and hybrid subset selection procedures for VAR models via the adaptive Lasso. By a proper choice of tuning parameters, one can identify the correct subset and obtain the asymptotic normality of the nonzero parameters with probability tending to one. Simulation results show that for small samples, a particular hybrid procedure has the best performance in terms of prediction mean squared errors, estimation errors and subset selection accuracy under various settings. The proposed method is also applied to modeling the IS-LM data for illustration.