simHawkes-class {eNchange} | R Documentation |

## 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

```
pw.hawk.obj <- new("simHawkes")
pw.hawk.obj@cp.loc <- 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)
```

[Package

*eNchange* version 1.0

Index]