SAPP (version 1.0.4)

linsim: Similation of a Self-exciting Point Process

Description

Perform simulation of a self-exciting point process whose intensity also includes a component triggered by another given point process data and a non-stationary Poisson trend.

Usage

linsim(data, interval, c, d, ax, ay, at, ptmax)

Arguments

data

point process data.

interval

length of time interval in which events take place.

c

exponential coefficient of lgp corresponding to simulated data.

d

exponential coefficient of lgp corresponding to input data.

ax

lgp coefficients in self-exciting part.

ay

lgp coefficients in the input part.

at

coefficients of the polynomial trend.

ptmax

an upper bound of trend polynomial.

Value

in.data

input data for sim.data.

sim.data

self-exciting simulated data.

Details

This function performs simulation of a self-exciting point process whose intensity also includes a component triggered by another given point process data and non-stationary Poisson trend. The trend is given by usual polynomial, and the response functions to the self-exciting and the external inputs are given the Laguerre-type polynomials (lgp), where the scaling parameters in the exponential functions, say $c$ and $d$, can be different.

References

Y.Ogata, K.Katsura and J.Zhuang (2006) Computer Science Monographs, No.32, TIMSAC84: STATISTICAL ANALYSIS OF SERIES OF EVENTS (TIMSAC84-SASE) VERSION 2. The Institute of Statistical Mathematics.

Y.Ogata (1981) On lewis' simulation method for point processes. IEEE information theory, vol. it-27, pp. 23-31.

Y.Ogata and H.Akaike (1982) On linear intensity models for mixed doubly stochastic poisson and self-exciting point processes. J. royal statist. soc. b, vol. 44, pp. 102-107.

Y.Ogata, H.Akaike and K.Katsura (1982) The application of linear intensity models to the investigatio of causal relations between a point process and another stochastic process. Ann. inst. statist math., vol. 34. pp. 373-387.

Examples

  data(PProcess)   ## The point process data
  linsim( PProcess, 20000, 0.13, 0.026,
          c(0.035,-0.0048), c(0.0,0.00017), c(0.007,-0.00000029), 0.007 )