I am working on a problem of predicting event counts based on user history.
This is a classical time series analysis problem, and I used the ARIMA model: (wiki).
I also applied a Hawkes point process model for the same purpose. Therein I predict all the points using a univariate Hawkes process and calculate counts.
However, I do not understand the fundamental difference between these two models;
I do know that ARIMA takes previous event counts as input, and the Hawkes model takes event timestamps as input.
Would someone please point out what the other differences between these models are?