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

## 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

 `1` ```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., H.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

 ```1 2 3``` ```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) ```

### Example output

```\$in.data
[1]   379.980   462.150   527.722   589.106   679.200  1281.589  1936.376
[8]  1978.485  2005.724  2046.084  2396.726  3363.897  3391.844  3415.762
[15]  3437.722  3574.983  3944.206  4343.578  5012.513  5183.430  5930.347
[22]  5979.053  6478.570  7166.254  7766.953  7770.460  7880.454  8053.839
[29]  8228.121  8832.647  9032.490  9643.708 10040.988 10361.319 11932.021
[36] 12116.334 12649.290 12694.823 13249.371 13274.072 14324.904 14333.882
[43] 14419.576 14649.989 15200.213 15724.547 15796.184 15805.969 15993.236
[50] 16010.848 16258.003 16311.447 16567.033 17070.861 17393.063 17400.454
[57] 17525.027 17857.488 18513.795 18961.702 19058.008 19157.142 19274.173
[64] 19416.957 19505.986 19569.694 19741.299 19812.689 19895.271

\$sim.data
[1]   272.6740   288.4796   289.4585   429.1059   569.3960   703.0780
[7]   765.8105   775.2845   806.5467   807.3006   861.7112   913.8867
[13]  1081.6380  1153.2642  1327.6080  1364.3403  1482.2084  1536.6699
[19]  1746.0608  1992.6499  2021.0105  2084.2810  2287.4811  2545.4863
[25]  2744.1549  2989.9092  3068.9358  3252.1822  3374.9241  3382.6042
[31]  3449.4929  3919.4678  3964.4710  4827.2374  5210.1790  5281.0843
[37]  5539.6956  5663.3850  5737.6040  6057.9333  6061.3940  6061.9298
[43]  6063.8387  6431.3542  6857.6799  6860.0080  6988.2674  6992.4195
[49]  7033.4842  7065.9623  7111.2394  7570.6837  7599.4876  7967.5065
[55]  8187.7243  8383.7132  8599.2303  8952.5807  9799.5396 10086.7045
[61] 10107.3036 10218.8555 10292.9053 10592.4653 11322.5214 11329.7593
[67] 11665.7319 11666.9163 12587.1471 12621.8663 12718.9385 13106.7651
[73] 13290.0210 13362.3787 13860.0081 13996.2822 14498.0605 14651.9229
[79] 14738.0583 14924.6213 15473.6836 15595.5387 15817.0662 15878.9656
[85] 15905.5431 15905.6837 16288.6194 16346.8540 16573.4838 16695.3875
[91] 17450.9296 17485.1872 17486.4130 17554.9584 17657.4724 17894.3734
[97] 18261.6920 18871.8166 19094.4277 19945.5896
```

SAPP documentation built on May 30, 2017, 2:32 a.m.