Spatiotemporal Hawkes processes is a self-exciting point process model, and has found myriad applications in earthquake aftershock and crime forecasting.
This Matlab package is developed for the following paper:
Baichuan Yuan, Hao Li, Andrea Bertozzi, P. Jeffrey Brantingham, and Mason Porter,
Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction,
to appear in SIAM Journal on Mathematics of Data Science, 2019.
Please cite this paper if you find the code useful.
A multivariate spatiotemporal Hawkes process (STHP) is characterized via its conditional intensity:
\lambda_u(t,x,y) = \mu_u(x,y) + \sum_{t>t_i} K_{u_iu} g(x-x_i,y-y_i,t-t_i)\,.
We estimate the triggering matrix K, background rate \mu_u and triggering kernel g from the observed data (X_i,y_i,t_i).
All these Matlab functions are documented. To get started, run the script test.m Please find the helper texts at the beginning of each M-file for more options.
To estimate a multivariate STHP given observed point processes data H(i,:)=(u(i), t(i), x(i), y(i)) i = 1,...,N. Here u(i) is the subprocess for event i.
[A,B,omega,sig,tau,aic,p,pb] = stestim(H)
or:
res=nphawkes(H)
To simulate multivariate STHPs:
y=simu_spetas(X,Y,T,mu,A,sigma,omega);
Please refer to the documentation for more options. A summary of the functions in this package is listed below:
User functions (API):
nphawkes.m: an EM-based nonparametric estimation for multivariate STHPstestim.m: an EM-based parametric estimation for multivariate STHPsimu_spetas.m: a Poisson clustering process based simulations for multivariate STHPtempestim.m: an EM-based parametric estimation for multivariate THP