Vector autoregressive model-order selection from finite samples using Kullback's symmetric divergence

In this paper, a new small-sample model selection criterion for vector autoregressive (VAR) models is developed. The proposed criterion is named Kullback information criterion (KIC_vc), where the notation vc stands for vector correction, and it can be considered as an extension of the KIC, for VAR models. KIC_vc adjusts KIC to be an unbiased estimator for the variant of the Kullback symmetric divergence, assuming that the true model is correctly specified or overfitted. Furthermore, KIC_vc provides better VAR model-order choices than KIC in small samples. Simulation results show that the proposed criterion selects the model order more accurately than other asymptotically efficient methods when applied to VAR model selection in small samples. As a result, KIC_vcserves as an effective tool for selecting a VAR model of appropriate order. A theoretical justification of the proposed criterion is presented.