Hawkes Process#

Simulate and visualise paths

# Author: Dialid Santiago <d.santiago@outlook.com>
# License: MIT
# Description: Simulate and visualise a Hawkes Process

from aleatory.processes import HawkesProcess
from aleatory.styles import qp_style

qp_style()  # Use quant-pastel-style

p = HawkesProcess()
fig = p.draw(N=200, T=10.0, colormap="Purples", figsize=(12, 7))
fig.show()

$Hawkes Process $N(t)$ with conditional Intensity process $\lambda_t^{\star} = 1.0 + \sum_{T_i < t} 1.0\exp(-1.0(t-T_i)) $ , Simulated Paths $N_t, t \leq T$, $N_T$ Marginal$

p = HawkesProcess(mu=0.5, alpha=1.0, beta=2.0)
fig = p.draw(N=200, T=10.0, colormap="Purples", mode="steps+points", figsize=(12, 7))
fig.show()

$Hawkes Process $N(t)$ with conditional Intensity process $\lambda_t^{\star} = 0.5 + \sum_{T_i < t} 1.0\exp(-2.0(t-T_i)) $ , Simulated Paths $N_t, t \leq T$, $N_T$ Marginal$

fig = p.plot(N=10, T=10.0, figsize=(10, 6))
fig.show()

$Hawkes Process $N(t)$ with conditional Intensity process $\lambda_t^{\star} = 0.5 + \sum_{T_i < t} 1.0\exp(-2.0(t-T_i)) $$

Total running time of the script: (0 minutes 3.844 seconds)

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