# linsim: Simulation of a Self-Exciting Point Process In SAPP: Statistical Analysis of Point Processes

 linsim R Documentation

## 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.