A note on transfer function model specification with noisy closed-loop input data

We assume that the input in a transfer function noise model is determined by a proportional-integral-derivative controller that is subject to noise. We show how such a noisy feedback in the input series affects the standard Box-Jenkins method of specifying the transfer function model. Our findings have important implications for the analyst who uses the traditional Box-Jenkins approach. The analyst will be led to estimate an incorrect transfer function model if feedback (exact or noisy) is present. Copyright (C) 2009 John Wiley & Sons, Ltd.