What are AIC and BIC in time series?

Akaike’s information criterion (AIC) compares the quality of a set of statistical models to each other.

• For example, you might be interested in what variables contribute to low socioeconomic status and how the variables contribute to that status.

• Let’s say you create several regression models for various factors like education, family size, or disability status; The AIC will take each model and rank them from best to worst.

• The “best” model will be the one that neither under-fits nor over-fits.

• AIC

• K = number of estimated parameters in the model

• L = Maximised likelihood function for the estimated model

$$AIC = 2k - 2ln(L)$$

The Bayesian Information Criterion (BIC) can be defined as:

$$k*log(n)- 2log(L(θ̂))$$

• K is the number of parameters that your model estimates.

• θ is the set of all parameters.

• L (θ̂) represents the likelihood of the model tested, when evaluated at maximum likelihood values of θ.