AbstractIn a previous paper, the author discussed what induction period was necessary when simulating time series models, in order to avoid distortion caused by the initial transients which arise from starting up a simulation run. That approach, however, can be misleading and this paper gives an alternative and more precise treatment which provides greater insight. One novel conclusion is that the necessary warm up period depends not only on the process to be simulated, but also on the length of the required simulation run. For simplicity, the detailed argument is restricted to the first order autoregressive model.