SAPP (version 1.0.9-1)

linsim: Simulation 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)

Value

in.data

input data for sim.data.

sim.data

self-exciting simulated data.

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.

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

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

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

Ogata, Y. and Akaike, H. (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.

Ogata, Y., Akaike, H. and Katsura, K. (1982) The application of linear intensity models to the investigation 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, interval = 20000, c = 0.13, d = 0.026, ax = c(0.035, -0.0048), 
       ay = c(0.0, 0.00017), at = c(0.007, -0.00000029), ptmax = 0.007)