Three-photon cascade from single self-assembled InP quantum dots. J. Persson, T. Aichele, V. Zwiller, L. Samuelson and O. Benson in Phys. Rev. B 69:233314 (2004).  What the paper says?

The simplified decay-chain of the tri-exciton is assumed as follows:

This is simplified since the exciton is in fact split in four levels and the excited bi-exciton in eight, due to spin interactions.

The $g^{(2)}(\tau)$ of autocorrelation are not those expected for a~$N=5$ cascade, most certainly due to re-excitations from one level to that next upstream dominating the dynamics, as opposed to actual (complete) cascades:

This also explains why cross-correlations were between neighbours only:

Comment on the discontinuity at $\tau=0$:

The analytic solution is basically a sum of exponentials: