Good evening everybody,
I would like run a Monte Carlo simulation with the following code. My problem is that I have to define kind of "double" loop, one for the time "t" and the other one for the "n" realization of the random variable rn. In the following my code WITHOUT Monte Carlo sampling (it works fine).
T=10000;
sigma=0.157;
k=0.3;
beta=0.99;
po=0.35;
phipi=1.5;
phiz=0;
B2=[sigma 1-beta*phipi; k*sigma k+beta*(sigma+phiz)]
B1=1/(sigma+phiz+k*phipi)
B=B1*B2
y=NaN(2,T)
y(1,1)=0.1
y(2,1)=0.2
kappa=[1/(sigma+phiz+phipi*k); k/(sigma+phiz+phipi*k)]
rn=randn(1,T)
a=NaN(2,T);
a(1,1)=1
a(2,1)=2
for t=2:T
y(:,t)=B*a(:,t-1)+kappa*rn(:,t);
a(:,t)=a(:,t-1)+t^(-1)*(y(:,t)-a(:,t-1));
end
stz=a(1,:)'
stpi=a(2,:)'
In the following instead "what I am trying to do". Bear in mind that I would like to obtain a multidimensional vector defined as y(2,T,N) in order to plot a "density function" of the realizations of the components of vector y (that is, the two variables z e pi).
T=100;
sigma=0.157;
k=0.3;
beta=0.99;
po=0.35;
phipi=1.5;
phiz=0;
B2=[sigma 1-beta*phipi; k*sigma k+beta*(sigma+phiz)]
B1=1/(sigma+phiz+k*phipi)
B=B1*B2
y=NaN(2,T)
y(1,1)=0.1
y(2,1)=0.2
kappa=[1/(sigma+phiz+phipi*k); k/(sigma+phiz+phipi*k)]
rn=randn(1,T)
a=NaN(2,T);
a(1,1)=1
a(2,1)=2
N=100
for n=1:N
rn=randn(1,N)
for t=2:T
y(:,t,n)=B*a(:,t-1)+kappa*rn(:,t);
a(:,t)=a(:,t-1)+t^(-1)*(y(:,t)-a(:,t-1));
end
end
Am I doing well? Another problem is that I cannot push the simulation above N=100 or T=100 (it is seems to me that N e T must agree, am I right?) otherwise it take too much time to compute.
What command I am supposed to use in Matlab to plot a density function of the MC simulation?
Thank you everybody
