Some relations between the various criteria for autoregressive model order determination

The problem of model order determination in autoregressive (AR) modeling of a given time series is considered. It is shown analytically that the model order selected using the final prediction error (FPE) criterion never exceeds the model order selected using the Akaike information criterion (AIC). It is further shown that under certain conditions, the model order selected using the criterion autoregressive transfer function (CAT) never exceeds the model order selected using the FPE criterion. These relations give some indication to what should be the preferred criterion, at least for the extreme cases when the model order is likely to be underestimated or overestimated.