Concepts Surrounding First Two Samples in Difference Equation I'm attempting to construct a difference equation in matlab for the function u(n) and find the auto-correlation matrix R.

I'm following the technique as is defined by my text below:



The system I'm trying to model is also defined by the text below. My a1 and a2 are different.



I have it defined in Matlab as is shown below and included results for my auto-correlation matrix. Let me clarify that I know that technically R is wrong because I'm not computing the expected value. I hadn't figured out how to do that yet and am attempting to tackle what I perceive to be the larger problem first.:

a1 = 0.1;
a2 = -0.72;

m_max = 101; % Sample Length

v = randn(1,m_max); % Create m samples of Gaussian white noise                
                % with 0 mean and unit variance

u = zeros(1,m_max); % Temp matrix for input vector

for n=3:m_max
    u(n) = v(n) - a1*u(n-1) - a2*u(n-2);
end

n = [1:1:m_max]; % Reconstruct n matrix to plot

u = transpose(u);
u_H = u';

R = u*u_H; % Corrleation Matrix

figure(1);
plot(v);
axis([1 m_max -5 5]);




This runs without any problem, but the issue is that my first two values are always zero. This makes sense in context of the code because I made the zero, but I know conceptually my correlation matrix R, as is shown by image 1 above,should not be 0 for r(0). Because my for loop thought must start from 3 (because u(n-2) is not defined for n&lt;3) I'll always have 0's in my R matrix. I suspect that I would need to know initial values but those aren't provided to me by the problem. Am I thinking about this incorrectly? Any help would be much appreciated. Thanks!
This is just the transient effect of the filter due to zero initial conditions. The "solution" is to throw away the first two zero samples of $u[n]$ because they are not related to the input noise signal $v[n]$.