A note on discriminating Poisson processes from other point processes with stationary inter arrival times

We give a universal discrimination procedure for determining if a sample point drawn from an ergodic and stationary simple point process on the line with finite intensity comes from a homogeneous Poisson process with an unknown parameter. Presented with the sample on the interval [0,t] the discrimination procedure gt, which is a function of the finite subsets of [0,t], will almost surely eventually stabilize on either POISSON or NOTPOISSON with the first alternative occurring if and only if the process is indeed homogeneous Poisson. The procedure is based on a universal discrimination procedure for the independence of a discrete time series based on the observation of a sequence of outputs of this time series.