The weighted average information criterion for order selection in time series and regression models

We propose a consistent criterion for model order selection in the model identification phase of time series and regression, based on a weighted average of an asymptotically efficient selection criterion, AICC (bias-corrected Akaike information criterion) and a consistent selection criterion, BIC (Akaike's Bayesian modification of AIC). The weights attached to AICC and BIC are optimal choices from a natural class of possible weights, and are proportional to the model-complexity penalty term of AICC and BIC, respectively. Thus, the AICC part of the criterion receives most of the weight for small sample size n, and the BIC part receives the most weight for large n. It is shown that this weighted average criterion, WIC, is essentially equivalent to AICC for small n and to BIC for large n. An extensive simulation study comparing the performance of WIC with several popular criteria has been done. It clearly shows that WIC is a very reliable and practical criterion. In particular, for small n, WIC performs as well as AICC and outperforms other criteria, and for large n, WIC performs as well as BIC and outperforms other criteria. This demonstrates the overall strength of WIC.