eNchange (version 1.0)

simHawkes-class: An S4 class for a nonstationary ACD model.

Description

A specification class to create an object of a simulated piecewise constant Hawkes model of order (1,1). We consider the following time-varying piecewise constant Hawkes process (which we term tvHawkes) \(\lambda({\upsilon}) = \lambda_0({\upsilon}) +\sum_{{\upsilon}_t < s} \alpha({\upsilon})e^{-\beta({\upsilon}) ({\upsilon}-{\upsilon}_t)}, \ \mbox{for} \ {\upsilon} = 1, \ldots,T\).

Value

Returns an object of simHawkes class.

Slots

H

The durational time series.

cH

The psi time series.

horizon

The time horizon of a Hawkes process typically expressed in seconds. Effective sample size will differ depending on the size of the parameters.

N

Effective sample size which differs depending on the size of the parameters.

cp.loc

The vector with the location of the changepoints. Takes values from 0 to 1 or NULL if none. Default is NULL.

lambda_0

The vector of the parameters lambda_0 in the Hawkes model as in the above formula.

alpha

The vector of the parameters alpha in the Hawkes model as in the above formula.

beta

The vector of the parameters beta in the Hawkes model as in the above formula.

References

Korkas Karolos. "Ensemble Binary Segmentation for irregularly spaced data with change-points" Preprint.

Examples

# NOT RUN {
pw.hawk.obj <- new("simHawkes")
[e-mail] <- c(0.5)
pw.hawk.obj@lambda_0 <- c(1,2)
pw.hawk.obj@alpha <- c(0.2,0.2)
pw.hawk.obj@beta <- c(0.7,0.7)
pw.hawk.obj@horizon <- 1000
pw.hawk.obj <- pc_hawkessim(pw.hawk.obj)
ts.plot(pw.hawk.obj@H)
ts.plot(pw.hawk.obj@cH)
# }