Simulate Hawkes process with non constant baseline¶

import numpy as np
import matplotlib.pyplot as plt

from tick.base import TimeFunction
from tick.hawkes import SimuHawkesExpKernels

from tick.plot import plot_point_process

period_length = 100
t_values = np.linspace(0, period_length)
y_values = 0.2 * np.maximum(
    np.sin(t_values * (2 * np.pi) / period_length), 0.2)
baselines = np.array(
    [TimeFunction((t_values, y_values), border_type=TimeFunction.Cyclic)])

decay = 0.1
adjacency = np.array([[0.5]])

hawkes = SimuHawkesExpKernels(adjacency, decay, baseline=baselines, seed=2093,
                              verbose=False)
hawkes.track_intensity(0.1)
hawkes.end_time = 6 * period_length
hawkes.simulate()

fig, ax = plt.subplots(1, 1, figsize=(10, 4))

plot_point_process(hawkes, ax=ax)

t_values = np.linspace(0, hawkes.end_time, 1000)
ax.plot(t_values, hawkes.get_baseline_values(0, t_values), label='baseline',
        ls='--', lw=1)
ax.set_ylabel("$\lambda(t)$", fontsize=18)
ax.legend()

plt.title("Intensity Hawkes process with exponential kernel and varying "
          "baseline")
fig.tight_layout()
plt.show()