whittle: Fitting Hawkes processes from discrete data
In hawkesbow: Estimation of Hawkes Processes from Binned Observations

Description Usage Arguments Details Value See Also Examples

This function fits a Hawkes process to discrete data by minimizing the Whittle contrast.

1	whittle(counts, kern, binsize = NULL, trunc = 5L, init = NULL, ...)

`counts`	A bin-count sequence
`kern`	Either a string (partially) matching one of the kernels implemented (see Details), or an object of class Model
`binsize`	(Optional) The bin size of the bin-count sequence; if omitted, defaults to 1 if `kern` is a string, or uses the member `binsize` of `kern` if it is of class Model
`trunc`	(Optional) The number of foldings taken into account due to aliasing
`init`	(Optional) Initial values of the optimisation algorithm
`...`	Additional arguments passed to `optim`

If specified as string, the argument kern must match (partially) one of the following (upper cases not taken into account): Exponential, SymmetricExponential, Gaussian, PowerLaw, Pareto3, Pareto2, Pareto1. The periodogram used in the optimisation procedure is computed in complexity O(n \log n), using function fft.

Returns a list containing the solution of the optimisation procedure, the object Model with its parameters updated to the solution, and the output produced by optim.

hawkes() for the simulation of Hawkes processes, discrete() for the discretisation of simulated Hawkes processes, Model for the abstract class, and Exponential for the specific reproduction kernels.

# Simulate and fit a Hawkes process with exponential kernel
x = hawkes(1000, fun = 1, repr = .5, family = "exp", rate = 1)
y = discrete(x, binsize = 1)
opt = whittle(y, "Exponential")
opt$par      # Estimated parameters


# May take up to 20 seconds
# Simulate and fit a Hawkes process with power law kernel
x = hawkes(1000, fun = 1, repr= .3, family = "powerlaw", shape = 3.5, scale = 1.0)
y = discrete(x, binsize = 1)
opt = whittle(y, "powerlaw")
opt$par      # Estimated parameters