Two-step adaptive model selection for vector autoregressive processes

Model selection (lag order selection and coefficient matrices substructures determination) is an integral part of statistical analysis of vector autoregression (VAR) models. This paper proposes a two-step shrinkage method for VAR model selection. The proposed method can be implemented through a simple algorithm. The resulting estimator is unbiased and subset-selection consistent, and the estimator of the nonzero components of the true parameter vector has asymptotically normal distribution. Limited finite sample Monte Carlo studies suggest that the proposed method outperforms existing alternatives in terms of accuracy in lag order estimation, forecasting and impulse response analysis. We also apply the proposed method to a multivariate macroeconomic time series for illustration.