Selecting the order of autoregressive models from small samples

The weak parameter criterion WPC is introduced as a means for model order selection. It is based on the same principles as Mallows' C
p
and the FPE and AIC criteria of Akaike. According to the WPC, parameters are weak and should be removed if the squares of their estimates are less than twice the expectation for a white noise signal. Roughly speaking, the square of an estimate must exceed twice its variance. Due to the conceptual simplicity, this criterion remains useful for small samples where the asymptotical properties are no longer valid. If the maximum order considered is
\sqrt{N}
or less, the difference between Akaike's FPE and AIC criteria on one hand and the WPC on the other hand remains small and the use of AIC or FPE may be justified. However, it is advised to use the WPC for higher maximum orders. By using different variances in the WPC for Yule-Walker and for Burg estimates, it is achieved that the average selected WPC order in small samples depends mainly on the given data and no longer on the method of parameter estimation.