Characteristics and moment estimators of temporal rainfall models such as Poisson rectangular pulse (PRP), Neyman‐Scott white noise (NSWN), and Neyman‐Scott rectangular pulse (NSRP) are investigated. It is shown that PRP and NSWN have a correlation structure like that of an autoregressive moving average (ARMA) (1,1) model whereas the NSRP has a dependence structure like that of an ARMA (2, 2). The admissible regions of lag‐1 and lag‐2 autocorrelations are derived to demonstrate that in general they are more restricted than their ARMA counterparts. An additional property denoted as variance ratio, which is intimately related to the scale of fluctuation of a process, is defined and used for model comparison. The bias and mean square error properties of the moment estimators are investigated with emphasis on the NSWN model, for which it is suggested that the temporal scale T, defined by βT = 1, provides the most efficient estimators of the parameters. Parameter β defines the arrival of rain bursts relative to the origin of storm systems. All three models are fitted to an extensive data set covering hourly precipitation data at 38 stations in northeastern Colorado. The correlation and variance ratio plots are used to select the appropriate model for each month. However, it is shown that the diurnal periodicity of storm occurrence is predominant during the summer months, which is a characteristic not built into any of the temporal models used here. Copyright 1987 by the American Geophysical Union.
