AIC=ln (sm2) + 2m/T
where m is the number of parameters in the model, and
sm2 is (in an AR(m) example) the estimated residual
variance: sm2 = (sum of squared residuals for model
m)/T. That is, the average squared residual for model m.
The criterion may be minimized over choices of m to form a tradeoff between the fit of the model (which lowers the sum of squared residuals) and the model's complexity, which is measured by m. Thus an AR(m) model versus an AR(m+1) can be compared by this criterion for a given batch of data.
An equivalent formulation is this one: AIC=T ln(RSS) + 2K where K is the number of regressors, T the number of obserations, and RSS the residual sum of squares; minimize over K to pick K.(Econterms)
Terms related to Akaike's Information Criterion: