numericalHawkes

This repository contains:

• A discrete implementation of the Hawkes process.
• A simulation for the Hawkes process which returns the branching structure.
• A demo showing how to use this code.

Usage:

Required packages:

• python3
• numpy
• scipy
• tick

Tutorial:

Preliminary

Load tick.base.TimeFunction, Hawkes and numpy.

from tick.base import TimeFunction
from Hawkes import Hawkes
import numpy as np

Define a Hawkes process

The baseline and triggering kernel are defined by tick.base.TimeFunction. Both functions are defined piecewise (discrete).

For example, a power function on can be realized as

ts = np.append([0],np.logspace(-5,np.log10(np.pi),256))
ys = 0.21/(ts+0.05)**1.1
phi = TimeFunction([ts, ys], inter_mode=TimeFunction.InterConstRight, dt=1e-6)
mu = TimeFunction([ts, 5*np.ones(len(ts))], inter_mode=TimeFunction.InterConstRight, dt=1e-6)
hawkes = Hawkes(mu,phi)

Simulation

The simulation returns a time sequence and the corresponding triggering relations.

t,p = hawkes.simulation(np.pi)

Todo

• Test