| simulateHawkes {hawkes} | R Documentation |
Hawkes process simulation Function
Description
The function simulates a Hawkes process for the given parameter, and until a time horizon.
Usage
simulateHawkes(lambda0, alpha, beta, horizon)
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. |
horizon |
Time horizon until which the simulation is to be conducted. |
Details
Notice that in the scalar case, one must have beta>alpha for the process to be stable, and in the multivariate case, the matrix (diag(beta)-alpha) must have eigen values with strictly positive real parts for the process to be stable.
Value
Returns a vector of jump times in the monovariate case, and a list of such vectors for every component in the multivariate case.
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
horizon<-3600#one hour
h<-simulateHawkes(lambda0,alpha,beta,horizon)
#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)
horizon<-3600#one hour
h<-simulateHawkes(lambda0,alpha,beta,horizon)