setCarmaHawkes: Hawkes Process with a Continuous Autoregressive Moving...

In yuima: The YUIMA Project Package for SDEs

Hawkes Process with a Continuous Autoregressive Moving Average(p, q) Intensity

Description

'setCarmaHawkes' describes a self-exciting Hawkes process where the intensity is a CARMA(p,q) process. The model admits the Hawkes process with exponential kernel as a special case but it is able to reproduce a more complex time-dependence structure

Usage

setCarmaHawkes(p, q, law = NULL, base.Int = "mu0", 
ar.par = "a", ma.par = "b", Counting.Process = "N", 
Intensity.var = "lambda", Latent.var = "x", time.var = "t", 
Type.Jump = FALSE, XinExpr = FALSE)

Arguments

p	a non-negative integer that indicates the number of the autoregressive coefficients.
q	a non-negative integer that indicates the number of the moving average coefficients.
law	An object of yuima.law-class that describes the jump size. If it is NULL, the jump size is unitary.
base.Int	a character-string that is the label of the baseline Intensity parameter. Defaults to "mu0".
ar.par	a character-string that is the label of the autoregressive coefficients. The default Value is ar.par="a".
ma.par	a character-string that is the label of the moving average coefficients. The default Value is ma.par="b".
Counting.Process	a character-string that is the label of the Counting process. Defaults to "N".
Intensity.var	a character-string that is the label of the Intensity process. Defaults to "lambda"
Latent.var	a character-string that is the label of the unobserved process. Defaults to "x".
time.var	the name of the time variable.
Type.Jump	a logical value. If it is TRUE, the jump size is deterministic.
XinExpr	a logical variable. The default value XinExpr=FALSE implies that the starting condition for Latent.var is zero. If XinExpr=TRUE, each component of Latent.var has a parameter as a initial value.

Value

Model an object of yuima.carmaHawkes-class.

Author(s)

The YUIMA Project Team

Contacts: Lorenzo Mercuri [e-mail]

References

Mercuri, L., Perchiazzo, A., & Rroji, E. (2022). A Hawkes model with CARMA (p, q) intensity. Insurance: Mathematics and Economics, 116, 1-26. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.insmatheco.2024.01.007")}.

Examples

## Not run: 
# Definition of an Hawkes with exponential Kernel
mod1 <- setCarmaHawkes(p = 1, q = 0)

# Definition of an Hawkes with a CARMA(2,1) Intensity process
mod2 <- setCarmaHawkes(p = 2, q = 1)

## End(Not run)

yuima documentation built on April 16, 2025, 5:12 p.m.