Effect of model structure and signal-to-noise ratio on finite-time uncertainty bounding in prediction error identification

In prediction error identification, confidence regions are most commonly derived from the asymptotic statistical properties of the parameter estimator. Therefore, these confidence regions are only asymptotically valid and, for finite samples, their actual coverage rate can be smaller than the desired coverage rate. In this paper, we analyze the influence of the SNR and of the type of model structure on the difference between the actual and desired coverage rates. In addition, we propose alternatives to the classical approach to constructing probabilistic confidence regions for Box-Jenkins systems.