Akaike's Information Criterion (AIC) provides a measure of model
quality by simulating the situation where the model is tested on a
different data set. After computing several different models, you
can compare them using this criterion. According to Akaike's theory,
the most accurate model has the smallest AIC.

Note:
If you use the same data set for both model estimation and validation,
the fit always improves as you increase the model order and, therefore,
the flexibility of the model structure.

Akaike's Information Criterion (AIC) is defined by the following
equation:

where V is the loss function, d is
the number of estimated parameters, and N is
the number of values in the estimation data set.

The loss function V is defined by the following
equation:

where represents the
estimated parameters.

For d<<N:

Note:AIC is approximately equal to log(FPE).

References

Ljung, L. System Identification: Theory for the User,
Upper Saddle River, NJ, Prentice-Hal PTR, 1999. See sections about
the statistical framework for parameter estimation and maximum likelihood
method and comparing model structures.