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 it 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. In this paper we propose the use of a sequence of tests to analyse the order selected with FPE. The result is a new identification criterion. In a simulation study, this criterion is shown to reach a compromise with respect to the above-mentioned trade-off. Some asymptotic properties are also derived.