def fit(self, timestamps):
"""
Parameters
----------
timestamps : list of float
Ordered list containing event times.
"""
self.res = self._estimator.fit(timestamps)
self.estimator = self.res.x
self.estimated_loss = self.res.fun
if self.return_model:
self.model = exp_thinning_hawkes(self.estimator[0],
self.estimator[1],
self.estimator[2])
self.model.set_time_intensity(timestamps)
import numpy as np
from code.hawkes_process import exp_thinning_hawkes
from code.estimator_class import loglikelihood_estimator
if __name__ == "__main__":
# Set seed
np.random.seed(7)
lambda_0 = 1.2
alpha = -0.4
beta = 0.9
# Create timestamps from exponential Hawkes process
hawkes = exp_thinning_hawkes(lambda_0, alpha, beta, max_jumps=100)
hawkes.simulate()
tList = hawkes.timestamps
# Estimate using the estimator class, the L-BFGS-B algorithm and the real loglikelihood
model = loglikelihood_estimator()
model.fit(tList)
print("Estimated parameters are:", model.estimator
) # Estimated parameters are: [ 1.49351268 -0.35849889 0.43911736]
print(
"With a loglikelihood of:",
-model.estimated_loss) # With a loglikelihood of: -112.56222084709412
import numpy as np
from matplotlib import pyplot as plt
from code.hawkes_process import exp_thinning_hawkes
if __name__ == "__main__":
# Set seed
np.random.seed(0)
lambda_0 = 1.05
alpha = -0.7
beta = 0.8
# Create a process with given parameters and maximal number of jumps.
hawkes = exp_thinning_hawkes(lambda_0=lambda_0,
alpha=alpha,
beta=beta,
max_jumps=15)
hawkes.simulate()
# Plotting function of intensity and step functions.
hawkes.plot_intensity()
plt.show()
arrowprops=dict(arrowstyle='|-|,widthA=0.3,widthB=0.3', facecolor='red'),
annotation_clip=False) # This enables the arrow to be outside of the plot
ax.annotate(parameters_str[i % 3], xy=(positions1[i] - 0.1, 1.5e-6), xytext=(positions2[i] - 0.8, 1.5e-6),
annotation_clip=False)
legend_str = ['exact', "approx"]
legend_elements = [Patch(facecolor=colors[i], edgecolor='k', label=legend_str[i]) for i in range(2)]
ax.legend(handles=legend_elements, loc='best')
ax.grid()
ax.set_yscale('log')
## Plot intensity examples for each parameter set.
for i in range(prefixed):
np.random.seed(1)
hawkes = exp_thinning_hawkes(theta_list[i, 0], theta_list[i, 1], theta_list[i, 2], max_jumps=max_jumps)
hawkes.simulate()
hawkes.plot_intensity(ax=intensity_ax[i], plot_N=False)
intensity_ax[i].set_xlim(0, 20)
intensity_ax[i].legend().set_visible(False)
intensity_ax[i].set_title(str(round(100 * proportion_list[i], 4)) + "%")
intensity_ax[0].set_ylim(0.475, 0.5001)
## Save image as pdf.
# plt.savefig('intensity_boxplot_log_cropped.pdf', bbox_inches='tight', format="pdf")
plt.show()