Bias of the corrected AIC criterion for underfitted regression and time series models

The Akaike Information Criterion, AIC (Akaike, 1973), and a bias-corrected version, Aicc (Sugiura, 1978; Hurvich & Tsai, 1989) are two methods for selection of regression and autoregressive models. Both criteria may be viewed as estimators of the expected Kullback-Leibler information. The bias of AIC and AICC is studied in the underfitting case, where none of the candidate models includes the true model (Shibata, 1980, 1981; Parzen, 1978). Both normal linear regression and autoregressive candidate models are considered. The bias of AICC is typically smaller, often dramatically smaller, than that of AIC. A simulation study in which the true model is an infinite-order autoregression shows that, even in moderate sample sizes, AICC provides substantially better model selections than AIC.