A discrimination atlas for Hawkes-versus-Cox model selection: where self-excitation and latent-regime clustering can be told apart

Abstract

No published power curve exists for the Hawkes-versus-Cox discrimination problem, which is odd given how often the two are raced. This note supplies one: a known-truth atlas over sample size, branching ratio, ladder depth and design, in which every arm generates streams, every arm is refit to every stream, and a cell is called decidable only when the generating arm is recovered in at least 80 per cent of replications, with held-out conditional log-loss reported as a cross-check.

The map has three practical consequences. It gives the onset sample size at which each mechanism becomes recoverable; it locates the degenerate cell where a near-critical power-law Hawkes and a multiplicative cascade mutually mimic, and identifies time-asymmetry as the discriminator that survives there; and it shows that panel designs recover a shared regime that no single stream of the same total length can. It is offered as a reusable instrument: cite your cell before your verdict.