Overview of the program [linsim]

This program performs 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.   The trend is given by usual polynomial, and the response functions to the self-exciting and the external inputs are given by the Laguerre-type polynomials, where the scaling parameters in the exponential functions, say c and d, can be different. More detailed explanation of parameters and variables are given in the control file [linsim.init]. 

The simulated data are displayed on the console and also save in the file [linsim.print] with the same format as the original [work.data]. In order to view the graphical features of the data by using the program [pgraph], change the name of the file for the simulated data to [work.data]. Similarly, the data file of external input [linsim.data] can be also viewed by change its name to [work.data].

Finally, it should be noted that the parameters for simulation must be specified such that the conditional intensity function be positive throughout the simulation time interval.


     Structure of the program
          [linsim]
             |---[input]
             |---[initl]
             |---[simxx]----[comfac]
             |       |------[duf]
             |       |------[unifor]
             |       |------[fx]--------[ptrend]
             |
             |---[output]

Remarks:

1. The input data file for this program should be always named [linsim.data]. Before using any other data as the external input point process for the simulation, one must save the data in the required format and name the data file as [linsim.data]. 

2. The input control file chooses the combination of the trend, the self-exiting and the external input components and specifies necessary variables. 

3. Calculation outputs of [linsim] are stored by the name [linsim.print] in the directory of [Calculations].


This program was originally designed (January 1985) and revised (December 2005) by Yosihiko Ogata, and programmed and also reprogrammed by Koichi Katsura, Institute of Statistical Mathematics, Tokyo, Japan.

References

Ogata, Y. (1981). On Lewis' simulation method for point processes, IEEE Information Theory, 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. Roy. Statist. Soc. Ser. B, 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., 34. pp. 373-387.

Ogata, Y. and Katsura, K. (1986). Point process model with linearly parametrized intensity for the application to earthquake data, Essays in Time Series and Allied Processes (Festscrift for Prof.     E.J. Hannan), J. Gani and M.B. Priestley eds., J. Appl. Probab. 23A, pp. 291-310.



