A new method for modelling the dynamics of rain measurement processes is suggested. The method takes the discrete nature and autocorrelation of measurements from the tipping bucket rain gauge into consideration. The considered model is a state space model with a Poisson marginal distribution. In the model there is only one parameter, a thinning parameter. The model is tested on 39 rain events. The estimated value for the various rain events is reflecting a subjective classification of rain events into frontal and convective rain. Finally, it is demonstrated how the model can be used for simulation and prediction.