Hawkes simulation with exotic kernels¶

import matplotlib.pyplot as plt
import numpy as np

from tick.base import TimeFunction
from tick.hawkes import SimuHawkes, HawkesKernelExp, HawkesKernelTimeFunc
from tick.plot import plot_point_process

t_values = np.array([0, 1, 1.5], dtype=float)
y_values = np.array([0, .2, 0], dtype=float)
tf1 = TimeFunction([t_values, y_values],
                   inter_mode=TimeFunction.InterConstRight, dt=0.1)
kernel_1 = HawkesKernelTimeFunc(tf1)

t_values = np.array([0, .1, 2], dtype=float)
y_values = np.array([0, .4, -0.2], dtype=float)
tf2 = TimeFunction([t_values, y_values], inter_mode=TimeFunction.InterLinear,
                   dt=0.1)
kernel_2 = HawkesKernelTimeFunc(tf2)

hawkes = SimuHawkes(
    kernels=[[kernel_1, kernel_1], [HawkesKernelExp(.07, 4), kernel_2]],
    baseline=[1.5, 1.5], verbose=False, seed=23983)

run_time = 40
dt = 0.01
hawkes.track_intensity(dt)
hawkes.end_time = run_time
hawkes.simulate()

fig, ax = plt.subplots(hawkes.n_nodes, 1, figsize=(14, 8))
plot_point_process(hawkes, t_max=20, ax=ax)

plt.show()