IHSEP (version 0.3.1)

IHSEP-package: 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 \([0,T]\).

Author

Feng Chen <[e-mail]>

Maintainer: Feng Chen <[e-mail]>

Details

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

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

if (FALSE) {
## 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)")
curve(100*(2+cos(2*pi*x)),add=TRUE,col="red")

## 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
}