Vectorization of a loop that uses past values

Is it possible to vectorize a loop if it uses past values? When iterations have a large number, simulation takes time to finish which i want to avoid. But i couldn't understand how to vectorize a loop when it has a past value.

N=100;
iterations=20000;
x=randn(1,N);
x=[x zeros(1,iterations-N)];
out=0;
sig=zeros(1,length(x)+1);
y=zeros(1,N+1);

for i=1:iterations
   out=x(i) +0.5*(y(N)+y(N+1));
   y=[out, y(1:length(y)-1)];
   sig(i) =out;
end

Answer 1

[Dinesh Yadav]

You cannot vectorize the above code as you have cyclic dependency in your code.