This work studies k-step-ahead prediction error model identification and its relationship to MPC control. The use of error criteria in parameter estimation will be discussed, where the identified model is used in model predictive control (MPC). Assume that the model error is dominated by the variance part, it can be shown that a k-step-ahead prediction error model is not optimal for k-step-ahead prediction. A normal one-step-ahead prediction error criterion will be optimal for k-step-ahead prediction. Then it is argued that even when some bias exists, the result could still hold true. Therefore, for MPC identification of linear processes, one-step-ahead prediction error models fever k-step-ahead prediction models. Simulations and industrial testing data will be used to illustrate the idea. (C) 2013 Elsevier Ltd. All rights reserved.