Hypotheses Testing: Poisson Versus Self-exciting

Abstract

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