Compute the likelihood function of a hawkes process

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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

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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

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#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)