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 © 2009 John Wiley & Sons, Ltd.