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Definition of Akaike's Information Criterion


Definition: Akaike's Information Criterion is a criterion for selecting among nested econometric models. The AIC is a number associated with each model:

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)

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