Akaike Information Criterion - AICc

AICc

AICc is AIC with a correction for finite sample sizes:

where n denotes the sample size. Thus, AICc is AIC with a greater penalty for extra parameters.

Burnham & Anderson (2002) strongly recommend using AICc, rather than AIC, if n is small or k is large. Since AICc converges to AIC as n gets large, AICc generally should be employed regardless. Using AIC, instead of AICc, when n is not many times larger than k2, increases the probability of selecting models that have too many parameters, i.e. of overfitting. The probability of AIC overfitting can be substantial, in some cases.

Brockwell & Davis (2009, p. 273) advise using AICc as the primary criterion in selecting the orders of an ARMA model for time series. McQuarrie & Tsai (1998) ground their high opinion of AICc on extensive simulation work with regression and time series.

AICc was first proposed by Hurvich & Tsai (1989). Different derivations of it are given by Brockwell & Davis (2009), Burnham & Anderson, and Cavanaugh (1997). All the derivations assume a univariate linear model with normally distributed errors (conditional upon regressors); if that assumption does not hold, then the formula for AICc will usually change. Further discussion of this, with examples of other assumptions, is given by Burnham & Anderson (2002, ch. 7). In particular, bootstrap estimation is usually feasible.

Note that when all the models in the candidate set have the same k, then AICc and AIC will give identical (relative) valuations. In that situation, then, AIC can always be used.