Modeling and simulating Poisson processes having trends or nontrigonometric cyclic effects

We formulate a nonparametric technique for estimating the (cumulative) mean-value function of a nonhomogeneous Poisson process having a long-term trend or some cyclic effect(s) that may lack familiar trigonometric characteristics such as symmetry over the corresponding cycle(s). This multiresolution procedure begins at the lowest level of resolution by estimating any long-term trend in the target counting process; then at progressively higher levels of resolution, the procedure yields estimates of the cyclic behavior associated with progressively smaller cycle lengths. We also formulate an efficient algorithm for generating realizations of such counting processes.