Overview of the program [linsim]

This program performs the simulation of bi-variate Hawkes' mutually exciting point processes. Non-stationary Poisson trends can also be included in the both intensity functions. The trend is given by usual polynomial and the response functions of the self-exciting and the input are given by the Laguerre-type polynomials, where the scaling parameters in the exponential function, say c, d, c2 and d2, can be different. More detailed explanation of parameters and variables are given in the control file [simbvh.init]. 

The simulated data can be seen in the calculated print, which is saved as the name [simbvh.print]. In order to view the graphical features of the data, save each of the two components of the simulated data as the name of [work.data] with the same format as the original [work.data], and use program [pgraph]. 

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

          [simbvh]
             |---[input]
             |---[initl]
             |---[simda]----[comfac]
             |      |-------[duf]
             |      |-------[unifor]
             |      |-------[fx]-------ptrend]
             |
             |---[output]

Remarks:

1. No input data file for this program is necessary.

2. The input control file [simbvh.init] selects a simulation of either self-exciting point processes or self and mutually exciting processes and also specifies necessary variables.

3. Calculatation records of [simbvh] are stored in [simbvh.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.

References

Hawkes, A.G. (1971). Spectra of some self-exciting and mutually exciting point processes, Biometrika, 58, pp. 83-90.

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.



