emhawkes (version 0.9.0)

hspec-class: An S4 class to represent an exponential marked Hawkes model

Description

This class represents a specification of a marked Hawkes model with exponential kernel. The intensity of the ground process is defined by: $$\lambda(t) = \mu + \int ( \alpha + \Psi ) * exp( -\beta (t-u)) d N(t).$$ For more details, please see the vignettes.

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 represets mark for counting process

impact

a function that describe the after impact of mark to lambda

Details

\(\mu\) is base intensity. This is generally a constant vector but can be extended to stochastic processes.

\(\alpha\) is a constant matrix which represents impacts on intensities after events. It is represented by slot mu.

\(\Psi\) is for non-constant parts of the impact. It may depend on any information generated by \(N\), \(\lambda\), \(k\) and so on. It is represented by slot impact.

\(\beta\) 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.

Examples

# NOT RUN {
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)

# }