This paper provides a coherent collection of metaphors and physical analogies which help to explain the nature of the processes depicted by autoregressive integrated moving average (ARIMA) models and which help in deriving their forecast functions. ARIMA models are widely used in the social sciences; but, all too often, their predictions go awry. In seeking to determine whether major errors of prediction are due to the inapproriateness of the models or to a failure to apply them correctly, it is useful to bear in mind their physical analogies.