Correlated input and output sequences of industrial processes are often autocorrelated. Analysts who wish to construct models for such processes from input and output sequences alone must be careful as the autocorrelations in individual time series can masquerade as cross-correlations. Several different models may appear equally plausible, depending on how the process had been operated. In this paper we study the input and output sequences from two industrial case studies using various time series tools. The results of our study illustrate that in feedback situations, where the current input is adjusted—either automatically or manually—on the basis of past output, different models may fit the data equally well. Which of these models describe the actual transfer function is unclear, unless a known dither signal can be added to the input to allow for an unambiguous identification of the transfer function. This problem is related to spurious regression and is of interest to econometricians who often deal with time series where feedback, known or unknown, may be responsible for misleading interpretations. Copyright © 2010 John Wiley & Sons, Ltd.