simNSMHP {MRHawkes}

Simulate a (bivariate) non-stationary multivariate Hawkes process (NSMHP)

Description

Simulate a bivariate non-stationary multivariate Hawkes process (NSMHP) with given given baseline intensity functions and self-excitation functions using the cascading structure of the process.

Usage

simNSMHP(TT = 100,
        nu1 = function(t) 0.6*exp(-t),
        nu2 = function(t) 0.2*exp(-t),
        g11 = function(t) 0.6*exp(-t),
        g12 = function(t) 0.2*exp(-t),
        g21 = function(t) 0.1*exp(-t),
        g22 = function(t) 0.5*exp(-t))

Arguments

TT

A scalar. The censoring time.

nu1

Basline intensity function for type one events.

nu2

Basline intensity function for type two events.

g11

Self-exciting function for type one events given the parent is a type two event.

g12

Cross-exciting function for type one events given the parent is a type two event.

g21

Cross-exciting function for type two events given the parent is a type one event.

g22

Self-exciting function for type two events given the parent is a type two event.

Details

The function works by simulating generation 0 events according to independent Poisson processes with the baseline intensity functions; then keep simulating future generation events as long as the number of the previous generation events of any type is non-zero. For each event type, we simulate these events according to M independent Poisson processes with the appropriate excitation intensity. When this recursive process stops, return events of all generations with their respective type labels as the events of the NSMHP on the interval (0,T].

Value

offspr1

All offspring events of type one

offspr2

All offspring events of type two

Author(s)

Tom Stindl <[e-mail]> Feng Chen <[e-mail]>

Examples

  B <- 10; i <- 0;
  data <- replicate(B, 
                    {cat(i<<-i+1,'\n'); 
                    simNSMHP(TT = 100)
                    })