simbvh: Simulation of Bi-Variate Hawkes' Mutually Exciting Point...

In SAPP: Statistical Analysis of Point Processes

Simulation of Bi-Variate Hawkes' Mutually Exciting Point Processes

Description

Perform the simulation of bi-variate Hawkes' mutually exciting point processes. The response functions are parameterized by the Laguerre-type polynomials.

Usage

simbvh(interval, axx = NULL, axy = NULL, axz = NULL, ayx = NULL, 
       ayy = NULL, ayz = NULL, c, d, c2, d2, ptxmax, ptymax)

Arguments

interval	length of time interval in which events take place.
axx	coefficients of Laguerre polynomial (lgp) of the transfer function (= response function) from the data events x to x (trf; x –> x).
axy	coefficients of lgp (trf; y –> x).
ayx	coefficients of lgp (trf; x –> y).
ayy	coefficients of lgp (trf; y –> y).
axz	coefficients of polynomial for x data.
ayz	coefficients of polynomial for y data.
c	exponential coefficient of lgp corresponding to xx.
d	exponential coefficient of lgp corresponding to xy.
c2	exponential coefficient of lgp corresponding to yx.
d2	exponential coefficient of lgp corresponding to yy.
ptxmax	an upper bound of trend polynomial corresponding to xz.
ptymax	an upper bound of trend polynomial corresponding to yz.

Value

x	simulated data X.
y	simulated data Y.

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, IT-27, pp.23-31.

Examples

simbvh(interval = 20000,
       axx = 0.01623,
       axy = 0.007306,
       axz = c(0.006187, -0.00000023),
       ayz = c(0.0046786, -0.00000048, 0.2557e-10),
       c = 0.4032, d = 0.0219, c2 = 1.0, d2 = 1.0,
       ptxmax = 0.0062, ptymax = 0.08)

SAPP documentation built on June 7, 2023, 5:45 p.m.