User`s guide

Using Akaike’s Criteria to Valida te Models
Akaike’s Information Criterion (AIC) is d efined by the following equation:
AIC V
d
N
=+log
2
where V is the loss function, d is the number of estimated parameters, and N
is the number of values in the estim ation data set.
The loss function V is defined by the following equation:
Vtt
N
NN
T
N
=
()()
()
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
∑
det , ,
1
1
εθ εθ
where
θ
N
represents the estimated parameters.
For d<<N:
AIC V
d
N
=+
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
log 1
2
Note AIC is approximately equal to log(FPE).
Computing AIC
Use the ai c command to compute Akaike’s Information Criterion (AIC) for
oneormorelinearornonlinearmodels,asfollows:
AIC = aic(m1,m2,m3,...,mN)
According to Akaike’s theory, the most accurate model has the smallest AIC.
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