An Improvement of Akaike's FPE Criterion to Reduce its Variability

The selection of the number of past observations to be included in a linear predictor (the order of the predictor) should be done with minimum variability, since this latter is not taken into account in the inference stage. For finite time series, there is a trade-off between variability and optimality (in the sense of mean squared prediction error). The widely used Akaike criteria, FPE and AIC, lead to highly variable estimated orders, whereas consistent criteria are downward biased when the optimal order increases with the sample size. We introduce a new automatic test procedure based on the FPE criterion which decreases the variability without biasing the selection by much.