In turbo machinery, clearance (the distance between the turbine or compressor blade tip to the casing) at high-pressure stages is one of the key design parameters to measure the turbine efficiency and effectiveness. Thus, appropriate modeling and prediction of the clearance under operational conditions is very important. If the clearance can be actively controlled, the turbine manufacturers get even more competitive advantages. For turbine design purpose, detailed physics based model is usually available. However, this kind of detailed model is not suitable for on-line prediction due to heavy computational requirements. Instead, a reduced order model based on the first order physics is used. Usually, the available reduced order models are computationally efficient, but they can hardly reach the accuracy desired by control engineers. In this paper, we applied an ARMA modeling technique for the reduced order clearance modeling and prediction. Typical turbine cycle operation data were used to build the ARMA model first. The built model is then used to predict other operations of the same unit, as well as other units of the same family.