# KS Test for Hawkes Process

I am analyzing some data by applying 1d-Hawkes processes. To evaluate the fit of the model itself (and particularly the chosen kernel, i.e. exponential), I am performing a KS test.

However, it is not entirely clear to me on which data the KS has to be performed. My understanding, at this point, is that the KS test has to be run on the interarrival times (first-order differences) of the model residuals. Is this correct?