hawkesbow (version 1.0.3)

compensator: Compensator of a Hawkes process

Description

Outputs the compensator (integrated intensity) of a Hawkes process.

Usage

compensator(x, t, fun = NULL, repr = NULL, family = NULL, M = NULL, ...)

Value

The compensator at time t.

Arguments

x

A non-negative numeric vector, sorted in ascending order; or an object of class "hawkes" output by function hawkes.

t

A non-negative numeric value or vector, at which the intensity should be computed.

fun

(default = TRUE) A non-negative numeric function or value - intensity (function) of the immigrant process.

repr

(default = NULL) A non-negative numeric value - mean number of offsprings.

family

(default = NULL) A character string "name" naming a distribution with corresponding distribution function dname, or directly the distribution function.

M

(default = NULL) A non-negative numeric value - upper bound on fun(ignored if fun is a numeric value).

...

Additional arguments passed on to the random generation function dname.

Examples

# Simulate an exponential Hawkes process with baseline intensity 1,
# reproduction mean 0.5 and exponential fertility distribution with rate 2.
x <- hawkes(10, fun=1, repr=0.5, family="exp", rate=2)
compensator(x, 0:10)
# Compensator with a different set of parameters
compensator(x, 0:10, repr=0.8, rate=3)
# Compensator with a different distribution function
compensator(x, 0:10, family="chisq", df=2)
# Simulate a Hawkes process with baseline intensity function 1 + sin(x),
# reproduction mean 0.5 and custom [0,1]-triangular fertility function.
x <- hawkes(10, fun=function(y) {1+sin(y)}, M=2, repr=0.5,
            family=function(n) {1 - sqrt(1 - runif(n))})
compensator(x, 0:10, family=function(y) ifelse(y>0 & y<1, 2-2*y, 0))