Description Details Slots Examples
This class represents a specification of a marked Hawkes model with exponential kernel. The intensity of the ground process is defined by:
λ(t) = μ + \int ( α + Ψ ) * exp( -β (t-u)) d N(t).
For more details, please see the vignettes.
μ is base intensity. This is generally a constant vector but can be extended to stochastic processes. Currently, piecewise constant mu is also possible. mu is left continous.
α is a constant matrix which represents impacts on intensities after events.
It is represented by slot mu
.
Ψ is for non-constant parts of the impact.
It may depend on any information generated by N, λ, k and so on.
It is represented by slot impact
.
β is a constant matrix for exponential decay rates.
It is represetned by slot beta
.
k is mark and represented by slot rmark
.
mu
, alpha
and beta
are required slots for every exponential Hawkes model.
rmark
and impact
are additional slots.
mu
numeric value or matrix or function, if numeric, automatically converted to matrix
alpha
numeric value or matrix or function, if numeric, automatically converted to matrix, exciting term
beta
numeric value or matrix or function, if numeric,, automatically converted to matrix, exponential decay
dimens
dimension of the model
rmark
a function that generates mark for counting process, for simulation
dmark
a density function for mark, for estimation
impact
a function that describe the after impact of mark to lambda
type_col_map
used for multiple kernel
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