linsim | R Documentation |

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.

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

`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. |

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.

`in.data` |
input data for |

`sim.data` |
self-exciting simulated data. |

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.

```
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)
```

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