hspec-class: An S4 class to represent an exponential marked Hawkes model
In emhawkes: Exponential Multivariate Hawkes Model

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

MU <- matrix(c(0.2), nrow = 2)
ALPHA <- matrix(c(0.75, 0.92, 0.92, 0.75), nrow = 2, byrow=TRUE)
BETA <- matrix(c(2.25, 2.25, 2.25, 2.25), nrow = 2, byrow=TRUE)
mhspec2 <- new("hspec", mu=MU, alpha=ALPHA, beta=BETA)