The Effect of Model-Selection Uncertainty on Autoregressive Models Estimates

Model-selection uncertainty corresponds to the uncertainty about the true lag order of the autoregressive process that should be picked. This paper shows that all model-selection criteria perform poorly in small samples. Model-selection uncertainty adds to the bias and variability in the coefficient estimates for these examples, and appears to be most relevant for small sample sizes, which is the case for most annual macro data. Even if we try to correct this bias using the bootstrap bias reduction method, the bootstrap bias-reduction method performs well in decreasing the bias of the coefficient estimates, but not without a cost. In particular, this method adds considerably to the variance and mean square error of these estimates. A comparison of several commonly used model-selection criteria shows that the SC outperforms the AIC and performs like the Shaos criterion with small subsample size. However, the Shaos criterion has to satisfy restrictive conditions. The SC is better than bootstrap model-selection criteria, such as the Shaos criterion, because the SC does not require subsampling when the optimal subsample is unknown. For larger subsample size, the AIC and SC outperform the Shaos criterion. Both the AIC and the Shaos criterion are inconsistent when I use the entire sample, but the Shaos criterion performs much worse than SC and AIC in that case. The problem is how to choose the optimal subsample size. Shaos criterion is very sensitive to the changes in the subsample size. Both the AIC and SC are computationally less demanding than Shaos criterion. Accordingly, the SC is preferable to the AIC and Shaos criterion