Regression and time series model selection in small samples

TLDR

The correction is particularly useful when the sample size is small or the number of fitted parameters is a moderate to large fraction of the sample size. A bias‑corrected AIC (AICC) is derived for regression and autoregressive time series models, and its application to nonstationary autoregressive and mixed ARMA models is discussed. AICC is asymptotically efficient for infinite‑dimensional true models and yields superior model‑order selection over other asymptotically efficient methods for finite‑dimensional true models.

Abstract

A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called AICC, is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, AICC is found to provide better model order choices than any other asymptotically efficient method. Applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed.