Hypotheses Testing: Poisson Versus Self-exciting

We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to the stationary Poisson process with known intensity. The alternatives are stationary self-exciting point processes. We consider one-sided parametric and one-sided non-parametric composite alternatives and construct locally asymptotically uniformly most powerful tests. The results of numerical simulations of the tests are presented. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..