A new criterion for modeling systems

The criterion that is proposed is an expected value of the mean square response error as an alternative to testing a model against new data. Modeling with respect to this new criterion does not change the estimate for a given model format from a maximum likelihood estimate or mean square response error estimate. The new criterion does, however, provide a means of comparing models with different formats and varying complexity. A numerical example is used to illustrate the application of the proposed criteria and the problem of searching for the best model. For all but the most trivial system identification problems, it is shown that a prohibitive number of combinations of terms of the model must be investigated to ensure the final model is best.