likelihoodHawkes: Compute the likelihood function of a hawkes process

In hawkes: Hawkes process simulation and calibration toolkit

Description

Compute the likelihood function of a hawkes process for the given parameter and given the jump times vector (or list of vectors in the multivariate case), and until a time horizon.

Usage

likelihoodHawkes(lambda0, alpha, beta, history)

Arguments

lambda0	Vector of initial intensity, a scalar in the monovariate case.
alpha	Matrix of excitation, a scalar in the monovariate case. Excitation values are all positive.
beta	Vector of betas, a scalar in the monovariate case.
history	Jump times vector (or list of vectors in the multivariate case).

Value

Returns the opposite of the likelihood.

References

Y. Ogata. (1981) On Lewis simulation method for point processes. IEEE Transactions on Information Theory, 31

Examples

#One dimensional Hawkes process
lambda0<-0.2
alpha<-0.5
beta<-0.7
history<-simulateHawkes(lambda0,alpha,beta,3600)
l<-likelihoodHawkes(lambda0,alpha,beta,history[[1]])

#Multivariate Hawkes process
lambda0<-c(0.2,0.2)
alpha<-matrix(c(0.5,0,0,0.5),byrow=TRUE,nrow=2)
beta<-c(0.7,0.7)
history<-simulateHawkes(lambda0,alpha,beta,3600)
l<-likelihoodHawkes(lambda0,alpha,beta,history)

Example output

hawkes documentation built on May 2, 2019, 5:17 p.m.