The natural variability of precipitation in agricultural regions both in time and space is modelled using extensions of Box & Jenkins (1976) methodology based on the ARMA procedure. This broad class of aggregate regional models belongs to the general family of Space-Time Autoregressive Moving Average (STARMA) processes. The paper develops a three-stage iterative procedure for building a ST ARMA model of multiple precipitation series. The identified model is STMA (13). The emphasis is placed on the three stages of the model building procedure, namely identification, parameter estimation and diagnostic checking. In the parameter estimation stage the polytope (or simplex) method and three further classical nonlinear optimization algorithms are used, namely two conjugate gradient methods and a quasi-Newton method. The polytope method has been adopted and the developed model performed well in describing the spatio-temporal characteristics of the multiple precipitation series. Application has been attempted in a rural watershed in southern Canada.