dm13450/hawkesprocesses.jl

MCMC Inference for a Hawkes process in Julia

HawkesProcesses

A Julia package for fitting, analysing and plotting Hawkes processes.

You can find the maths behind the algorithm here. The Bayesian sampling algorithm is a generic version of the bayesianETAS package from CRAN which can be found here.

Examples

• HawkesProcesses.jl: An Introduction
• Hawkes Processes and DIC
• Does a Terror Attack Lead to More Terror Attacks?

Features

I provide a number of different tools to both fit and analyse a collection of events using Hawkes processes.

Simulate a Hawkes process

bg = 0.5
kappa = 0.5
kernel(x) = pdf.(Distributions.Exponential(1/0.5), x)
maxT = 100
simevents = HawkesProcesses.simulate(bg, kappa, kernel, maxT)

Enhanced Bayesian Inference

Sample the parameters of a Hawkes process using the latent variable Bayesian MCMC algorithm. Currently only constant background, constant κ and exponential kernel are available, but this will be extend to generic functions in the future.

bgSamps, kappaSamps, kernSamps = HawkesProcesses.fit(simEvents, maxT, 1000)

Calculate the likelihood for a Hawkes process

likelihood = HawkesProcesses.likelihood(simevents, bg, kappa, Distributions.Exponential(1/0.5))

Intensity calculation

intensity = HawkesProcesses.intensity(ts, simevents, bg, kappa, kernel)

To Do

• Make functions consistent with Julia style guide.
• Check type safety
• Return parent vector from simulate.

Next Features

• Likelihood with functional background
• Generic Bayesian inference.

hawkesprocesses.jl's Issues

Online intensity calculation

I have yet to investigate myself, but I'm going to explore an online algorithm for calculating the intensity of an event series.

It should be pretty straightforward I imagine. Is there any objection to adding that to this lib?

Add parametric baseline intensity?

Hi Dean,

This looks like an awesome package and I'm excited to try it out! I'm interested in modeling citations with a Hawkes process where the baseline rate decays according to an exponential kernel as well, Something like:

$\mu_t= \alpha * \exp(-t * \delta) $

Any advice on how I might adapt the code to do something like this? Perhaps without estimating the delta parameter since I assume that complicates things?

Thanks in advance,
Bernie

Is this package under maintenance?

I found this package interesting. I am currently learning the application of hawkes processes on finance, and this one looks like a great place to start.

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