hspec-class: An S4 Class Representing an Exponential Marked Hawkes Model

In ksublee/emhawkes: Exponential Multivariate Hawkes Model

An S4 Class Representing an Exponential Marked Hawkes Model

Description

This class defines a marked Hawkes model with an exponential kernel. The intensity of the ground process is expressed as:

\lambda(t) = \mu + \int_{(-\infty,t)\times E} ( \alpha + g(u, z) ) e^{-\beta (t-u)} M(du \times dz).

For more details, refer to the vignettes.

Details

\mu is base intensity, typically a constant vector or a function.

\alpha is a constant matrix representing the impact on intensities after events, stored in the alpha slot.

\beta is a constant matrix for exponential decay rates, stored in the beta slot.

z represents the mark and can be generated by rmark slot.

g is represented by eta when it is constant, and by impact when it is a function.

mu, alpha and beta are required slots for every exponential Hawkes model. rmark and impact are additional slots.

Slots

mu

A numeric value, matrix, or function. If numeric, it is automatically converted to a matrix.

alpha

A numeric value, matrix, or function. If numeric, it is automatically converted to a matrix, representing the exciting term.

beta

A numeric value, matrix, or function. If numeric, it is automatically converted to a matrix, representing the exponential decay.

eta

A numeric value, matrix, or function. If numeric, it is automatically converted to a matrix, representing the impact of an additional mark.

impact

A function describing the after-effects of the mark on \lambda, with the first argument always being param.

dimens

The dimension of the model.

rmark

A function that generates marks for the counting process, used in simulations.

dmark

A density function for the mark, used in estimation.

type_col_map

A mapping between type and column number of the kernel used in multi-kernel models.

rresidual

A function for generating residuals, analogous to the R random number generator function, specifically for the discrete Hawkes model.

dresidual

A density function for the residual.

presidual

A distribution function for the residual.

model

A string.

Examples

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)
mhspec2

ksublee/emhawkes documentation built on Feb. 5, 2025, 1:35 a.m.