"""
============================
Fit Hawkes power law kernels
============================

This Hawkes learner based on conditional laws
(`tick.inference.HawkesConditionalLaw`) is able to fit Hawkes power law
kernels commonly found in finance applications.

It has been introduced in the following paper:

Bacry, E., & Muzy, J. F. (2014).
Second order statistics characterization of Hawkes processes and
non-parametric estimation. `arXiv preprint arXiv:1401.0903`_.

.. _arXiv preprint arXiv:1401.0903: https://arxiv.org/pdf/1401.0903.pdf
"""

import numpy as np
import matplotlib.pyplot as plt

from tick.hawkes import SimuHawkes, HawkesKernelPowerLaw, HawkesConditionalLaw
from tick.plot import plot_hawkes_kernels

multiplier = np.array([0.012, 0.008, 0.004, 0.005])
cutoff = 0.0005
exponent = 1.3

support = 2000

hawkes = SimuHawkes(
    kernels=[[
        HawkesKernelPowerLaw(multiplier[0], cutoff, exponent, support),
        HawkesKernelPowerLaw(multiplier[1], cutoff, exponent, support)
    ], [
        HawkesKernelPowerLaw(multiplier[2], cutoff, exponent, support),
        HawkesKernelPowerLaw(multiplier[3], cutoff, exponent, support)
    ]], baseline=[0.05, 0.05], seed=382, verbose=False)
hawkes.end_time = 50000
hawkes.simulate()

e = HawkesConditionalLaw(claw_method="log", delta_lag=0.1, min_lag=0.002,
                         max_lag=100, quad_method="log", n_quad=50,
                         min_support=0.002, max_support=support, n_threads=-1)

e.incremental_fit(hawkes.timestamps)
e.compute()

fig = plot_hawkes_kernels(e, log_scale=True, hawkes=hawkes, show=False,
                          min_support=0.002, support=100)
for ax in fig.axes:
    ax.legend(loc=3)
    ax.set_ylim([1e-7, 1e2])

plt.show()