User`s guide

8 Model Analysis
Vtt
N
NN
T
N
=
()()
()
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
∑
det , ,
1
1
εθ εθ
where
θ
N
represents the estimated parameters.
Computing FPE
You can compute A kaike’s Final Prediction Error (FPE) criterion for linear
and nonlinear models.
Note FPE for nonlinear A RX models that include a tree partition
nonlinearity is not supported.
To compute FPE, use the fpe command, as follows:
FPE = fpe(m1,m2,m3,...,mN)
According to Akaike’s theory , the most accurate model has the smallest FPE.
You can also access the FPE value of an estimated model by accessing the
FPE field of the Estimatio nInf o property of this model. For example, if you
estimated the model
m, you can access its FPE usin g the following com mand:
m.EstimationInfo.FPE
Definition of AIC
Akaike’s Information C riterion (AIC)providesameasureofmodelquality
by simulating the situation w here the model is teste d on a diffe rent data
set. After computing several different models, you can compare them using
this criterion. According to Akaike’s theory, the most accurate model h as
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 m odel order and, therefore, the
flexibility of the model structure.
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