Are PTA measurements sensitive to gravitational wave non-Gaussianities?

Observing non-Gaussianity in the timing residuals of Pulsar Timing Arrays (PTAs) has recently attracted attention as a potential discriminator between astrophysical and cosmological origins of the observed Gravitational Wave (GW) signal. In this work, we show that even in an idealized signal-dominated setup, after decorrelating data to avoid spurious detections, statistical tests applied to PTA data cannot distinguish between Gaussian and non-Gaussian GWBs in a model-agnostic way. In particular, without making strong assumptions on the GW spectrum or the properties of the population, the sensitivity to any distinctive non-Gaussian feature is washed out.