Turnout systems are one of the most critical systems on railway infrastructure. Diagnostics and prognostics on turnout system have ability to increase the reliability & availability and reduce the downtime of the railway infrastructure. Even though diagnostics on railway turnout systems have been reported in the literature, reported studies on prognostics in railway turnout system is very sparse. This paper presents autoregressive moving average model based prognostics on railway turnouts. The model is applied to data collected from real turnout systems. The failure progression is obtained manually using the exponential degradation model. Remaining Useful Life of ten turnout systems have been reported and results are very promising.