Plot estimated intensity of Hawkes processes¶

import matplotlib.pyplot as plt

from tick.hawkes import SimuHawkesSumExpKernels, HawkesSumExpKern
from tick.plot import plot_point_process

end_time = 1000

decays = [0.1, 0.5, 1.]
baseline = [0.12, 0.07]
adjacency = [[[0, .1, .4], [.2, 0., .2]], [[0, 0, 0], [.6, .3, 0]]]

hawkes_exp_kernels = SimuHawkesSumExpKernels(
    adjacency=adjacency, decays=decays, baseline=baseline, end_time=end_time,
    verbose=False, seed=1039)

hawkes_exp_kernels.track_intensity(0.1)
hawkes_exp_kernels.simulate()

learner = HawkesSumExpKern(decays, penalty='elasticnet', elastic_net_ratio=0.8)
learner.fit(hawkes_exp_kernels.timestamps)

t_min = 100
t_max = 200
fig, ax_list = plt.subplots(2, 1, figsize=(10, 6))
learner.plot_estimated_intensity(hawkes_exp_kernels.timestamps, t_min=t_min,
                                 t_max=t_max, ax=ax_list)

plot_point_process(hawkes_exp_kernels, plot_intensity=True, t_min=t_min,
                   t_max=t_max, ax=ax_list)

# Enhance plot
for ax in ax_list:
    # Set labels to both plots
    ax.lines[0].set_label('estimated')
    ax.lines[1].set_label('original')

    # Change original intensity style
    ax.lines[1].set_linestyle('--')
    ax.lines[1].set_alpha(0.8)

    # avoid duplication of scatter plots of events
    ax.collections[1].set_alpha(0)

    ax.legend()

fig.tight_layout()
plt.show()