Hypotheses Testing: Poisson Versus Self-exciting

TL;DR

This paper develops and evaluates statistically powerful tests to distinguish between stationary Poisson processes and self-exciting point processes, addressing a key problem in point process analysis.

Contribution

It introduces new locally asymptotically uniformly most powerful tests for hypotheses involving Poisson and self-exciting processes, including both parametric and nonparametric cases.

Findings

Numerical simulations demonstrate test effectiveness.

Tests achieve optimality in asymptotic regimes.

Applicable to both parametric and nonparametric models.

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.