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.