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170 Chapter 5 Modeling and Forecasting with ARMA Processes
AIC, and BIC criteria of Akaike and a bias-corrected version of the AIC known as
the AICC.
5.5.1 The FPE Criterion
The FPE criterion was developed by Akaike (1969) to select the appropriate order
of an AR process to fit to a time series {X1,...,Xn}. Instead of trying to choose the
order p to make the estimated white noise variance as small as possible, the idea is to
choose the model for {Xt} in such a way as to minimize the one-step mean squared
error when the model fitted to {Xt} is used to predict an independent realization {Yt}
of the same process that generated {Xt}.
Suppose then that {X1,...,Xn} is a realization of an AR(p) process with coefficients
φ1,...,φp, p