Glossary

Akaike's Information Criterion (AIC)

AIC is a model selection criterion that balances goodness of fit against model complexity. Given a set of candidate models, the one with the lowest AIC is preferred. AIC rewards fit through a likelihood term but penalises the number of estimated parameters to discourage overfi...

Definition

AIC is a model selection criterion that balances goodness of fit against model complexity. Given a set of candidate models, the one with the lowest AIC is preferred. AIC rewards fit through a likelihood term but penalises the number of estimated parameters to discourage overfitting. The penalty in AIC is smaller than in the Bayesian Information Criterion (BIC), making AIC relatively more tolerant of complex models.

Why It Matters

When researchers build time-series models or stepwise regressions, they need an objective way to choose among competing specifications. AIC provides a principled trade-off: a model that fits better but uses more parameters is only preferred if the improvement in likelihood outweighs the complexity penalty. It is especially common in lag-order selection for VAR and ARMA models.

Example

Suppose you are estimating a VAR model for Turkish inflation, industrial production, and the policy rate. You estimate versions with 1 through 6 lags. The AIC values are 120.3 (1 lag), 98.7 (2 lags), 95.1 (3 lags), 95.8 (4 lags), 97.2 (5 lags), and 99.0 (6 lags). The model with 3 lags has the lowest AIC and would be selected.

Related Terms

Software Notes

  • SPSS: Analyze > Regression > Linear; AIC is reported in model summary. Alternatively, use the STATS FIT extension.
  • R: Use AIC(model) after fitting with lm(), arima(), or VAR(). Compare models with AIC(model1, model2).
  • Stata: After estimation, run estat ic to display AIC and BIC. Use estimates store and lrtest for nested comparisons.