AIC

Definition

The Akaike Information Criterion (AIC) is a model selection criterion that balances model fit against complexity.

$AIC=-2\log L_{\max }+2k$

where:

• $L_{\max }$ = maximum likelihood
• $k$ = number of parameters ($p+q+1$ with constant, $p+q$ without)

Interpretation

• Lower AIC is better
• Penalizes models with more parameters
• Emphasizes prediction efficiency

Model Selection

Choose the model with minimum AIC among competing models.

Properties

Property	Description
Penalty	$2k$ — constant penalty per parameter
Best for	Prediction efficiency
Asymptotic	Not consistent (may overfit with large $n$)

Related

• BIC Criterion
• Box-Jenkins Strategy
• Model Selection via Data Splitting