System Identification Toolbox™

fpe - Akaike Final Prediction Error for estimated model

Syntax

fp = fpe(Model1,Model2,Model3,...)

Description

Model is any estimated idmodel (idarx, idgrey, idpoly, idproc, idss).

fp is returned as a row vector containing the values of the Akaike Final Prediction Error (FPE) for the different models. This is defined as

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

The loss function V is

where represents the estimated parameters.

FPE can be negative when the number of estimated parameters exceeds the number of data samples, which can occur for models with multiple outputs. For models with multiple output, the assumption that d/N is small is not valid. In when this assumption is not valid, use AIC instead.

References

Sections 7.4 and 16.4 in Ljung (1999).

See Also

freqresp

fselect