markov-modulated hawkes

[ayjab]

Hello,

I’m currently working on implementing a Markov-Modulated Hawkes Process (MM-Hawkes), where the intensity parameters (baseline and kernels) depend on a latent CTMC regime. I'd like to build on tick’s infrastructure particularly the multivariate Hawkes process with sum-of-exponentials kernels but I’m unsure how best to integrate the latent-state structure.

What I’m trying to do:

• For each hidden state s, I have a distinct set of parameters:
  $μᵢ^{(s)}(t), α_{ij}^{(s)}, β^{(s)}$

• The latent state $S_t$ follows a continuous-time Markov chain with generator Q.

• I’d like to alternate between:

  1. E-step: run forward–backward to infer the posterior over latent states,
  2. M-step: for each state, fit its Hawkes parameters using weighted event sequences. However, the .fit doesn't allow weights ofc.

• Is there a way to reuse tick.hawkes.HawkesSumExpKern to fit different parameters per latent state in a smart way?

• Has anyone tried integrating regime-switching or state-dependent intensities into the tick framework?

• Is there any way to make the baseline time-dependent?

Any guidance, ideas, or existing efforts I could build on would be really appreciated! Thanks!