A new approach to the problem of modelling and predicting respiration motion has been implemented. This is a dual-component model, which describes the respiration motion as a non-periodic time series superimposed onto a periodic waveform. A periodic autoregressive moving average algorithm has been used to define a mathematical model of the periodic and non-periodic components of the respiration motion. The periodic components of the motion were found by projecting multiple inhale–exhale cycles onto a common subspace. The component of the respiration signal that is left after removing this periodicity is a partially autocorrelated time series and was modelled as an autoregressive moving average (ARMA) process. The accuracy of the periodic ARMA model with respect to fluctuation in amplitude and variation in length of cycles has been assessed. A respiration phantom was developed to simulate the inter-cycle variations seen in free-breathing and coached respiration patterns. At±14% variability in cycle length and maximum amplitude of motion, the prediction errors were 4.8% of the total motion extent for a 0.5 s ahead prediction, and 9.4% at 1.0 s lag. The prediction errors increased to 11.6% at 0.5 s and 21.6% at 1.0 s when the respiration pattern had±34% variations in both these parameters. Our results have shown that the accuracy of the periodic ARMA model is more strongly dependent on the variations in cycle length than the amplitude of the respiration cycles.