hawkesbow (version 1.0.3)

hawkesbow-package: hawkesbow: Estimation of Hawkes Processes from Binned Observations

Description

Implements an estimation method for Hawkes processes when count data are only observed in discrete time, using a spectral approach derived from the Bartlett spectrum, see Cheysson and Lang (2020) <arXiv:2003.04314>. Some general use functions for Hawkes processes are also included: simulation of (in)homogeneous Hawkes process, maximum likelihood estimation, residual analysis, etc.

Author

Maintainer: Felix Cheysson (ORCID)

Details

To be implemented later:

• Variance and confidence interval for the estimated parameters

• Spectral density based goodness-of-fit tests

• Custom built-kernels

Examples

# Simulate an exponential Hawkes process with baseline intensity 1,
# reproduction mean 0.5 and exponential fertility function with rate 2.
x <- hawkes(10, fun=1, repr=0.5, family="exp", rate=2)

# Plot its conditional intensity function
oldpar = par()
par(mfrow = c(2, 1), mar = c(4.1, 4.1, 1.1, 2.1))
plot(x, intensity = TRUE)
# and its poisson cluster representation
plot(x, intensity = FALSE)
par(oldpar)

# Estimate the parameters from the arrival times of `x`
# using maximum likelihood estimation
opt = mle(x$p, "Exponential", x$end)
opt$par                          # Estimated parameters
opt$model$ddloglik(x$p, x$end)     # Hessian matrix of the log-likelihood

# Estimate the parameters from count data using Whittle's method
y = discrete(x, binsize = 1)
opt = whittle(y, "Exponential", binsize = 1)
opt$par                          # Estimated parameters