Specify exogenous function for Hawkes fitting

[andrei-rizoiu]

Hi, is it possible currently (or can we get this as a feature) to specify the exogenous (immigrant) intensity? This could be useful in real applications where the immigrants are either known or can be estimated.

Use case:
I know that my immigrants arrive following a given function (say sin(t) + 2). I'd like to be able to be able to:

• simulate a Hawkes process given the exogenous function and label the events as immigrants or offspring; and/or
• given a set of events (without the immigrant/offspring label), but knowing the immigrant intensity, fit the parameters of the Hawkes process.

[qykong]

Hi andrei, incorporating immigrants in the Hawkes processes is useful. It might be easier to start with the simulation whereas a bit more effort is involved in adding the fitting procedure for immigrants. I'll work on this recently

[andrei-rizoiu]

Sampling Hawkes realizations might also be tricky: one would need to first sample the immigrants, and then sample a Hawkes for each of the immigrants to generate the offspring.