I have some data and I would like to test the hypothesis that they come from a homogeneous Poisson process. I can of course look at the inter event times and test if these are exponentially distributed. However this misses lots of reasons why it might not be Poisson it seems . Is there a list of tests, or a particular good test, that I can use that does more than look at the set of inter event times between consecutive events?
If you take all the differences between arrival times, that is not just consecutive arrival times, can this be used to make a more powerful test for example?