Approximate system modeling and predictor complexity

The Minimum Prediction Error Method of deterministic and stochastic systems identification consists of selecting a model (i.e., predictor) for a given block of data such that a function of the prediction errors and a suitable measure of predictor complexity is minimized. In this context, the use of Algorithmic Complexity Theory to measure predictor complexity is examined. Further, it is shown that this approach is closely related to the Minimum Description Length principle of Rissanen, and that both specialize to the Maximum Likelihood technique. This set of ideas is then related to those in the formulation due to J. Maciejowski.