K-dimensional mutually exciting process with kernel matrix
\(\phi_{jk}(u) = a_{jk} \beta e^{-\beta u}\): MLE via the exact
log-likelihood with the O(n) exponential recursion per (j,k) pair.
Usage
morie_crim_hawkes_multivariate(times, marks, t_max = NULL, beta = NULL)
Arguments
- times
Numeric event times.
- marks
Integer/factor component labels (length of times).
- t_max
Observation horizon. Default max(times).
- beta
Fixed decay rate (shared); estimated when NULL via an
outer profile grid.
Value
List of class "morie_mv_hawkes": mu (K-vector),
A (KxK excitation matrix), beta, loglik, spectral_radius, n,
converged, call.
References
Hawkes (1971) Biometrika 58(1).
Examples
set.seed(2)
tt <- sort(runif(150, 0, 100)); mk <- sample(1:2, 150, TRUE)
morie_crim_hawkes_multivariate(tt, mk, beta = 1)
#> Multivariate Hawkes (K = 2, beta = 1), n = 150
#> mu: 0.7281 0.6693
#> A:
#> [,1] [,2]
#> [1,] 0.0000 0
#> [2,] 0.1697 0
#> spectral radius = 0.001
