| Library: | times |
| See also: |
| Quantlet: | simou | |
| Description: | Simulation of discrete observations of an Ornstein-Uhlenbeck process via its transition probability law. The simulated process follows the stochastic differential equation: dX(t) = aX(t) dt + s dW(t). |
| Usage: | x = simou(n,a,s,delta) | |
| Input: | ||
| n | scalar, (n+1) represents the number of observations | |
| a | scalar, drift parameter of the simulated Ornstein-Uhlenbeck process, a has to be smaller than 0 to make the process stationary | |
| s | scalar, diffusion parameter of the simulated Ornstein-Uhlenbeck process | |
| delta | scalar, time step size. The process is simulated at time points 0, delta, 2*delta, ..., n*delta | |
| Output: | ||
| x | (n+1)-dimensional vector, containing the simulated trajectory | |
randomize(123)
n = 1000 ; number of observations
a = -1 ; speed of adjustment
s = .1 ; diffusion coefficient
delta = 0.001 ; time step size
ou = simou(n,a,s,delta) ; simulation of a path of an OU process in [0,1](n*delta = 10)
time =(0:n)*delta ; time scale
library("plot")
d=createdisplay(1,1)
ouplot = setmask(time~ou,"line")
show(d,1,1,ouplot)
setgopt(d,1,1,"xlabel","time t","ylabel","X(t)")
setgopt(d,1,1,"yvalue",0|1)
A display containing a typical trajectory of an OU process in [0,1] is shown.