Theory and Methodology Modeling and Simulating Poisson Processes Having Trends or Nontrigonometric Cyclic E€ects

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 e€ect(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 ecient algorithm for generating realizations of such counting processes.