Some convergence properties of multi-step prediction error identification criteria

Multi-step prediction error identification methods are preferred over plain one-step ahead prediction error ones in application contexts (e.g., predictive control) where model accuracy is required over a wide horizon. For sufficiently high prediction horizons, their properties can be shown to be conveniently related to those of output error methods, for which several important issues (e.g., uniqueness of estimation, robustness with respect to the noise model) have been characterized in the literature. The convergence properties of such criteria with respect to the prediction horizon are analyzed.