A statistical model which captures the main features of hourly exposure series of global radiation is proposed. This model is used to obtain a procedure to generate radiation series without imposing, a priori, any restriction on the form of the probability distribution function of the series. The statistical model was taken from the stationary stochastic processes theory. Data were obtained from ten different Spanish locations. As monthly hourly exposure series of global radiation are not stationary, they are modified in order to remove the observed trends. A multiplicative autoregressive moving average model with regular and seasonal components was used. It is statistically accepted that this is the true model which generates most of the analyzed sequences. However, the underlying parameters of the model vary from one location to another and from one month to another. Therefore, it is necessary to examine further the relationship between the parameters of the model and the available data from most locations.