Order selection criteria for vector autoregressive models

The least-squares method for estimating the parameters of the vector autoregressive (VAR) model is considered and new estimates for the covariance matrix of the VAR model input noise and the prediction error covariance matrix are derived. Based on these new estimates, the criteria FPEF and AICF for VAR model order selection are proposed. FPEF can replace the final prediction error (FPE) criterion, and AICF, which is an estimate of the Kullback–Leibler index, can replace the Akaike information criterion (AIC) and its corrected version AICC. A simulation study shows that FPEF is less biased than FPE, and AICF is less biased than AIC and AICC. In addition, the performance of the proposed criteria is compared with that of other well-known criteria and the results show that AICF has the best performance and gives the smallest average prediction error.