@TechReport{ it:2022-009, author = {Torsten S{\"o}derstr{\"o}m and Umberto Soverini}, title = {Analyzing the Parameter Bias when an {ARMAX} Model is Fitted to Noise-Corrupted Data}, institution = {Department of Information Technology, Uppsala University}, department = {Division of Systems and Control}, year = {2022}, number = {2022-009}, month = oct, abstract = {When an ARMAX model is fitted to noise-corrupted data using the prediction error method, biased estimates are obtained. The bias is examined, with emphasis on the situation when the system is almost non-identifiable. In contrast to the case of using an output error model, no general results on the size of the bias seem to apply.} }