# IHSEP-package: Inhomogeneous Self-exciting Process In IHSEP: Inhomogeneous Self-Exciting Process

 IHSEP-package R Documentation

## Inhomogeneous Self-exciting Process

### Description

Simulates the (inhomogeneous) Self-exciting point process (SEPP), or Hawkes process, on [0,T] with a given (possibly time-varying) baseline/background intensity function nu and excitation function (fertility rate function) g. Or calculate the likelihood of an SEPP with baseline intensity nu and excitation function g for a given set of event times on [0,T].

### Details

 Package: IHSEP Type: Package Version: 1.0 Date: 2014-05-12 License: GPL(>=2)

### Author(s)

Feng Chen <feng.chen@unsw.edu.au>

Maintainer: Feng Chen <feng.chen@unsw.edu.au>

### References

Feng Chen and Peter Hall (2013). Inference for a nonstationary self-exciting point process with an application in ultra-high frequency financial data modeling. Journal of Applied Probability 50(4):1006-1024.

Feng Chen and Peter Hall (2016). Nonparametric Estimation for Self-Exciting Point Processes – A Parsimonious Approach. Journal of Computational and Graphical Statistics 25(1): 209-224.

Alan G Hawkes (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika 58(1):83-90.

### Examples

```## Not run:
## simulate the times of a Poisson process on [0,1] with intensity
## function nu(t)=100*(2+cos(2*pi*t)).
tms <- simPois(int=function(x)100*(2+cos(2*pi*x)),int.M=300)
## calculate a nonparametric estimate of the intensity function
int <- lpint::lpint(tms,Tau=1)
matplot(int\$x,int\$y+qnorm(0.975)*outer(int\$se,c(-1,0,1)),type="l",lty=c(2,1,2),
col=1,xlab="t",ylab="nu(t)")

## simulate an IHSEP on [0,1] with baseline intensity function
## nu(t)=100*(2+cos(2*pi*t)) and excitation function
## g(t)=0.5*8*exp(-8*t)
asep <- simHawkes1(nu=function(x)200*(2+cos(2*pi*x)),nuM=600,
g=function(x)8*exp(-16*x),gM=8)
## get the birth times of all generations and sort in ascending order
tms <- sort(unlist(asep))
## calculate the minus loglikelihood of an SEPP with the true parameters
mloglik1a(tms,TT=1,nu=function(x)200*(2+cos(2*pi*x)),
g=function(x)8*exp(-16*x),Ig=function(x)8/16*(1-exp(-18*x)))
## calculate the MLE for the parameter assuming known parametric forms
## of the baseline intensity and excitation functions
est <- optim(c(400,200,2*pi,8,16),
function(p){
mloglik1a(jtms=tms,TT=1,
nu=function(x)p[1]+p[2]*cos(p[3]*x),
g=function(x)p[4]*exp(-p[5]*x),
Ig=function(x)p[4]/p[5]*(1-exp(-p[5]*x)))
},
hessian=TRUE,control=list(maxit=5000,trace=TRUE))
## point estimate by MLE
est\$par
## standard error estimates:
diag(solve(est\$hessian))^0.5

## End(Not run)
```

IHSEP documentation built on Sept. 17, 2022, 1:05 a.m.