simbvh {SAPP}

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)