linsim: Simulation of a Self-Exciting Point Process

In SAPP: Statistical Analysis of Point Processes

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)

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.

Value

in.data	input data for sim.data.
sim.data	self-exciting simulated data.

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)

SAPP documentation built on June 7, 2023, 5:45 p.m.